@inproceedings(KleRaoRau94, author= "Philio Klein and Satish Rao and Monika Rauch", title= "Faster shortest-path algorithms for planar graphs", booktitle="Conference Proceedings of the Annual ACM Symposium on Theory of Computing 1994", annote= "It gives a linear-time algorithm for single-source shortest paths in planar graphs with nonnegative edge-lengths", year= "1994", pages= "27-37") @article(RamYan94, author= "Viiava Ramachandran and Haohua Yang", title= "Finding the closed partition of a planar graph", journal="Algorithmica", annote= "", volume= 11, year= "1994", pages= "443-468") @article(BooWes94, author= "Heather Booth and Jeffery Westbrook", title= "Linera algorithm for analysis of minimum spanning and shortest-path trees of planar graphs", journal="Algorithmica", annote= "", volume= 11, year= "1994", pages= "341-352") @article(CaiHanTar93, author= "Jiazhen Cai and Xiaofeng Han and Robert E. Tarjan", title= "O\((mlogn\))-time algorithm for the maximal planar subgraph problem", journal="SIAM Journal on Computing", annote= "An O\((mlogn\))-time algorithm for finding a maximal planar subgraph in a graph.", volume= 22, year= "1993", pages= "1142-1162") @inproceedings(ParPhi93, author= "james K. Park and Cynthia A. Phillips", title= "Finding minimum-quotient cuts in planar graphs", booktitle="Conference Proceedings of the Annual ACM Symposium on Theory of Computing 1993", annote= "", year= "1993", pages= "766-775") @inproceedings(Rao92, author= "Satsh B. Rao", title= "Faster algorithms for finding small edge cuts in planar graphs", booktitle="Conference Proceedings of the Annual ACM Symposium on Theory of Computing", annote= "", year= "1992", pages= "229-240") @article(MorSha91, author= "Craio A. Morqenstern and Henry D. Shapiro", title= "Heuristics for rapidly four-coloring large planar graphs", journal="Algorithmica", annote= "", volume= 6, year= "1991", pages= "869-891") @article(ShiWuKuo90, author= "Wei-Kuan Shih and Kuo Wu and Y. S. Kuo", title= "Unifying maximum cut and minimum cut of a planar graph", journal="IEEE Transactions on Computers", annote= "An O(\(n^{1.5}logn\)) algorithm for finding maximum cut in weighted planar graph", volume= 39, year= "1990", pages= "694-697") @article(Lau90, author= "Jean-Paul Laumond", title= "Connectivity of plane triangulations", journal="Information Processing letters", annote= "", volume= 34, year= "1990", pages= "87-96") @article(LinPro89, author= "Andrzei Lingas and Andrzei Proskurowski", title= "On parallel complexity of the subgraph homeomorphism and the subgraph isomorphism problem for classes of planar graphs", journal="Theoretical Computer Science", annote= "", volume= 68, year= "1989", pages= "155-173") @article(Hag90, author= "Torben Haoerup", title= "Optimal parallel algorithms on planar graphs", journal="Information and Computation ", annote= "An O(logn) algorithm with O(n+m) processors for finding connected components and spanning tree in planar graph", volume= 84, year= "1990", pages= "71-96") @article(KozKin85, author= "Krzysztof Kozminiski and Edwin Kinnen", title= "Rectangular duals of planar graphs", journal="Networks", annote= "", volume= 15, year= "1985", pages= "145-157") @article(Fre84, author= "Greg N. Frederickson", title= "On linear-time algorithms for five-coloring planar graphs", journal="Information Processing letters", annote= "O(n) algorithms", volume= 19, year= "1984", pages= "219-224") @inproceedings(Smi84, author= "Justin R. Smith", title= "Parallel algorithms for depth-first searches: I, planar graphs", booktitle="1984 ACM Twelfth Annual Computer Science Conference: The Future of computing . CSC '84 and SIGCSE Symposium", annote= "", year= "1984", pages= "171") @article(BecMeh86, author= "M Becker and K. Mehlhorn", title= "Algorithms for routing in planar graphs", journal="Acta informatica", annote= "", volume= 23, year= "1986", pages= "163-176") @article(Nao87, author= "Joseph Naor", title= "Fast parallel coloring of planar graphs with five colors", journal="Information processing letters", annote= "", volume= 25, year= "1987", pages= "51-53") @inproceedings(KleRei86, author= "Philip N. Klein and John H. Reif", title= "Efficient parallel algorithm for planarity", booktitle="Annual Symposium on Foundations of Computer Science (Proceedings) 27th", annote= "", year= "1986", pages= "465-477") @inproceedings(Fre87A, author= "Greg N. Federickson", title= "New approach to all paris shortest paths in planar graphs", booktitle="Conference Proceedings of the Annual ACM Symposium on Theory of Computing 19th", annote= "An O(\(n^2\)) algorithm for all paris shortest paths in planar graphs", year= "1987", pages= "19-28") @article(Bie86, author= "Daniel Bienstock", title= "Algorithm for reliablity analysis of planar graphs", journal="Networks", annote= "", volume= 16, year= "1986", pages= "411-422") @inproceedings(GazMil87, author= "Hillel Gazit and Gary L. Miller", title= "Parallel algorithm for finding a separator in planar graphs", booktitle="Annual Symposium on Foundations of Computer Science(Proceedings) 28th", annote= "", year= "1987", pages= "238-248") @inproceedings(Rao87, author= "Satish Rao", title= "Finding near optimal separators in planar graphs", booktitle="Annual Symposium on Foundations of Computer Science(Proceedings) 28th", annote= "", year= "1987", pages= "225-237") @article(Fre87B, author= "Greg N. Federickson", title= "Fast algorithms for shortes paths in planar graphs, with applications", journal="SIAM Journal on Computing ", annote= "It uses graph decomposition and data structure techniques to yield fast algorithm for a number of shortest path and related problems An O\(n\sqrt{logn})\) algorithm for single source problem, An O(\(n^2)\) algorithm for all pairs shortest pathes problem and an O(nlogn) algorithm for min cut problem", volume= 16, year= "1987", pages= "1004-1022") @article(HeYes88, author= "Sin He and Yaacov Yesha", title= "Nearly optimal parallel algorithm for constructing depth first spanning trees in planar graphs", journal="SIAM Journal on Computing", annote= "", volume= 17, year= "1988", pages= "486-491") @article(Sha88, author= "Gregory E. Shannon", title= "Linear-processor algorithm for depth-first search in planar graphs", journal="Infomatin Processing Letters", annote= "", volume= 29, year= "1988", pages= "119-123") @article(He88, author= "Xin He", title= "Nearly optimal parallel algorithm for constucting maximal independent set in planar graphs", journal="Theoretical Computer Science", annote= "", volume= 61, year= "1988", pages= "33-47") @article(AosIri77, author= "K. Aoshima and M Iri", title= " Comments on F. Hadlock's paper: ``Finding a maximum cut of a planar graph in polynomial time''", journal="SIAM-J.-Comput", annote= "", volume= 6, year= "1977", pages= "86--87") @article(Zam72, author= "Tudor Zamfirescu", title= "A two-connected planar graph without concurrent longest paths", journal="J.-Combinatorial-Theory-Ser", annote= "", volume= 13, year= "1972", pages= "116--121") @article(MatNisSai86, author= "Kazuhiko Matsumoto and Takao Nishizeki and Nobuji Saito", title= "Planar multicommodity flows, maximum matchings and negative cycles", journal="SIAM-Journal-on-Computing", annote= "This paper deals with the multicommodity flow problem on a class of planar graphs $G$", volume= 15, year= "1986", pages= "495--510") @article(GifFou84, author= "J. W. Giffin and L. R. Foulds", title= " Efficient graph planarity updating tests", journal="Ars-Combinatoria", annote= " The problem considered here is to exhibit a planar graph of maximal weight in a weighted clique", volume= 17, year= "1984", pages= "185--202") @article(Rei83, author= "John H. Reif", title= "Minimum $s-t$ cut of a planar undirected network in $O(n\,{\rm log}\sp{2}(n))$ time", journal="SIAM-Journal-on-Computing", annote= "This paper presents an $O(n\,{\rm log}\sp{2}(n))$ algorithm for computing a minimum (cost) s-t cut of a planar undirected network", volume= 12, year= "1983", pages= "71--81") @article(Glu82, author= "A. D. Glukhov", title= "On the maximum genus of plane graphs", journal=" Ukrainian Math", annote= "english translation : An algorithm for determining the maximum genus of a connected planar graph is described. Its complexity is polynomial", volume= 34, year= "1982", pages= "82 - 84") @article(Dji81, author= "H. N. Djidjev", title= " Separator theorems for planar graphs", journal="Doklady Bolgarskoi Akademii Nauk. Comptes Rendus de l'Academie Bulgare des Sciences", annote= "", volume= 34, year= "1981", pages= "163--164") @article(ColBoo81, author= "Charles J. Colbourn and Kellogg S. Booth", title= "Linear time automorphism algorithms for trees, interval graphs, and planar graphs", journal="SIAM-Journal-on-Computing", annote= "", volume= 10, year= "1981", pages= "203--225") @article(Shi80, author= "Yossi Shiloach", title= "A multiterminal minimum cut algorithm for planar graphs", journal="SIAM-Journal-on-Computing", annote= "This paper presents an algorithm for computing all minimum cuts between all pairs of vertices in an undirected connected planar graph having n vertices in time $O((n log n)^2)$", volume= 9, year= "1980", pages= "219--224") @article(ItaShi79, author= "Alon Itai and Yossi Shiloach", title= "Maximum flow in planar networks", journal="SIAM-Journal-on-Computing", annote= "", volume= 8, year= "1979", pages= "135--150") @article(He90, author= "Xin He", title= "An efficient algorithm for edge coloring planar graphs with $\Delta$ colors", journal="Theoretical-Computer-Science", annote= "`An efficient algorithm for edge coloring a planar graph $G$, the complexity of sequential implementation is O(n), the complexity of parallel implementation is $(log^2n)$ time with O(n) processors.", volume= 74, year= "1990", pages= " 299--312") @article(BerJohLeiShoSny90, author= "Fran Berman and David Johnson and Tom Leighton and Peter W. Shor and Larry Snyde", title= "Generalized planar matching", journal="Journal-of-Algorithms", annote= "", volume= 11, year= "1990", pages= "153--184") @article(dadKir90, author= "N. Dadoun and D. G. Kirkpatrick", title= " Parallel algorithms for fractional and maximal independent sets in planar graphs", journal="Discrete-Applied-Mathematics", annote= "The authors construct a simple parallel algorithm that finds a maximal (in the sense of inclusion) independent set in a planar graph. The time is $O(\log(n)\log\sp *(n))$ and the number of processors is linear", volume= 27, year= "1990", pages= "69--83") @article(ChroNis90, author= "Marek Chrobak and Takao Nishizeki", title= "Improved edge-coloring algorithms for planar graphs", journal="Journal-of-Algorithms", annote= "", volume= 11, year= "1990", pages= "102--116") @article(SuzAkaNis89, author= "Hitoshi Suzuki and Takehiro, Akama abd Takao Nishizeki", title= "Algorithms for finding internally disjoint paths in a planar graph", journal="[Electronics-and-Communications-in-Japan.-Part III:-Fundamental-Electronic-Science", annote= "Three efficient algorithms are presented for finding vertex-disjoint trees and internally disjoint paths in a planar graph.", volume= 72, year= "1989", pages= "55--67") @article(Ste89, author= "Iain A. Stewart", title= "An algorithm for colouring perfect planar graphs", journal="Information-Processing-Letters", annote= "We present an algorithm for properly colouring a perfect, planar graph $G$ using $\gamma(G)$ colours", volume= i31, year= "1989", pages= "97--101") @article(KleRei88, author= "Philip N. Klein and John H. Reif", title= "An efficient parallel algorithm for planarity", journal="Journal-of-Computer-and-System-Sciences", annote= "The authors describe a parallel algorithm for testing a planar embedding of a planar graph. Their algorithm finds a planar embedding of an $n$-node graph or reports that none exists in time $O(\log\sp 2n)$ using $n$ processors of a CREW-PRAM", volume= 37, year= "1988", pages= "190--246") @article(BieMon88, author= "Daniel Bienstock and Clyde L. Monma", title= "On the complexity of covering vertices by faces in a planar graph", journal="SIAM-Journal-on-Computing", annote= "", volume= 17, year= "1988", pages= "53--76") @article(Hor87, author= "J. D. Horton", title= "A polynomial-time algorithm to find the shortest cycle basis of a graph", journal="SIAM-Journal-on-Computing", annote= "It gives an algorithm to find a cycle basis with shortest possible length in O($m^3$n)", volume= 16, year= "1987", pages= "358--366") @article(Ree93, author= "Bruce Reed", title= "Rooted routing in the plane", journal="Centrum voor Wiskunde en Informatica. Centre for Mathematics and Computer Science. CWI Quarterl", annote= "The author describes an algorithm of the author et al. [in Graph structure theory (Seattle, WA, 1991), 295--301, Contemp. Math., 147, Amer. Math. Soc., Providence, RI, 1993; MR 94m:05067] for finding vertex-disjoint paths in a planar graph, given the end points. If the number of required paths is fixed, the algorithm is linear-time.", volume= 6, year= "1993", pages= "241--255") @incollection(Por92, author= "Oscar Porto", title= "Even induced cycles in planar graphs", booktitle=" Collection: LATIN '92 (Sao Paulo, 1992)", annote= "An $O(n\sp 3)$ algorithm for testing the existence of even induced cycles in planar graphs is presented", year= "1992", pages= "417--429") @incollection(KleSub93, author= "Philip N. Klein and Siram Subramanian", title= "A fully dynamic approximation scheme for all-pairs shortest paths in planar graphs", booktitle="Collection: Algorithms and data structures (Montreal, PQ, 1993)", annote= "We give a fully dynamic approximation scheme for maintaining all-pairs shortest paths in planar networks", year= "1993", pages= "442--451") @incollection(KaoTenToy93, author= "Ming Yang Kao and Shang Hua Teng and Kentaro Toyama", title= "Improved parallel depth-first search in undirected planar graphs", booktitle="Collection: Algorithms and data structures (Montreal, PQ, 1993)", annote= "", year= "1993", pages= "409--420") @incollection(Wes92, author= "Jeffery Westbrook", title= "Fast incremental planarity testing", booktitle="Collection: Automata, languages and programming (Vienna, 1992)", annote= "", year= "1992", pages= "342--353") @incollection(FurRag91, author= "Martin Furer and Balaji Raghavachari", title= "Contracting planar graphs efficiently in parallel", booktitle="Collection: Foundations of software technology and theoretical computer science (New Delhi, 1991)", annote= "Our algorithm contracts a given planar graph in $O(\log n)$ rounds to one with a constant number of vertices", year= "1991", pages= "319--335") @incollection(KanBod92, author= "Goos Kant and Hans L. Bodlaender", title= "Triangulating planar graphs while minimizing the maximum degree", booktitle=" Collection: Algorithm theory---SWAT '92 (Helsinki, 1992)", annote= "In this paper we study the problem of triangulating a planar graph $G$ while minimizing the maximum degree $\Delta(G')$ of the resulting triangulated planar graph $G'$. It is shown that this problem is NP-complete", year= "1992", pages= "258--271") @article(Har93, author= "David Hartvigsen", title= "Minimum path bases", journal="Journal-of-Algorithms", annote= "", volume= 15, year= "1993", pages= "125--142") @incollection(RipWagWei93, author= "Lipa Heike Ripphausen and Dorothea Wagner and Karsten Weihe", title= "The vertex-disjoint Menger problem in planar graphs", booktitle="Collection: Proceedings of the Fourth Annual ACM-SIAM Symposium on Discrete Algorithms (Austin, TX, 1993)", annote= "A linear time algorithm for finding the maximum number of vertex-disjoint paths between vertices $s$ and $t$ in a planar graph is presented", year= "1993", pages= "112--119") @article(Myr92, author= "Wendy Myrvold", title= " Counting $k$-component forests of a graph", journal="Networks", annote= "We describe an algorithm for computing the number of $k$-component spanning forests of a graph $G$ that runs in polynomial time for fixed $k$", volume= 22, year= "1992", pages= "647--652") @incollection(Gaz91, author= "Hillel Gazit", title= "A deterministic parallel algorithm for planar graphs isomorphism", booktitle="Collection: 32nd Annual Symposium on Foundations of Computer Science", publisher="San Juan, PR, 1991", annote= "We present a deterministic parallel algorithm to determine whether two planar graphs are isomorphic. The algorithm needs $O(\log n)$ separators that have to be computed one after the other. ", year= "1991", pages= "723--732") @article(GarJohTar76, author= "M.R. Garey and D. S. Johnson and R.E. Tarjan", title= "The planar Hamiltonian circuit problem is NP-complete", journal="SIAM Journal on Computing", annote= "Proof of that the planar Hamiltonian circuit problem is NP-complete", volume= 5, year= "1976", pages= "") @inbook(HopTar72, author= "H. Hopcrof and R. E. Tarjan", title= "Isomorphism of planar graph in :Miller and Tatcher eds", booktitle="Complexity of Computer Computation ", annote= "", year= "1972", pages= "") @article(HopTar74, author= "H. Hopcrof and R. E. Tarjan", title= "Efficient planarity testing", journal="Journal of ACM", annote= "An O(n) algorithm for testing if a graph is planar", volume= 21, year= "1974", pages= "") @article(ChiNisAbeOza85, author= "N. Chiba and T Nishizeki and S Abe and T Ozawa", title= "A linear algorithm for embedding planar graphs using PQ-tree", journal="J. comput system Sci.", annote= "An O(n) algorithm for embedding a planar graph", volume= 30, year= "1985", pages= "54--76") @article(JayThuSwa89, author= "R. Jayakumar and K. Thulasiraman and M. N. S. Swamy", title= "O($n^2$) algorithm for graph planarization ", journal="IEEE trans CAD", annote= "", volume= 8, year= "1989", pages= "257--267") @article(ChiNisSai81, author= "N. Chiba and T Nishizeki and N Saito", title= "A linear 5-coloring algorithm of planar graphs", journal="J algorithms", annote= "An O(n) algorithm of 5-coloring planar graphs", volume= 2, year= "1981", pages= "317--327") @techreport(MatShiTar80, author= "D. Matula and Y Shiloach and R Tarjan", title= "Two linear time algorithms for 5-coloring a planar graph", institution="Rept STAN-CS-80-830 Department of Computer Science, Stanford University ", annote= "", year= "1980", pages= "") @book(Ore67, author= "Oystein Ore", title="The four color problem", publisher="Academic Press", year= "1967") @article(LipMil78, author= "R. J. Lipton and T. E. Miller" , title= "A batching method for coloring planar graphs", journal="Inform Processing Lett", annote= "It gives an algorithm O(nlogn)find 5-coloring in planar graph", volume= 7, year= "1978", pages= "185-186") @article(HagChrDik89, author= "T Hagerup and M Chrobak and K Diks", title= "Optimal parallel 5-coloring of planar graphs ", journal="SIAM J Comput", annote= "An parallel 5-coloring algorithm of planar graphs , which take O(\(lognlogn^{*}n\)) steps with O(\(n/(lognlog^{*}n\)) processors. It does not require a planar embedding to be given as part of input.", volume= 18, year= "1989", pages= "288-300") @article(LipTar79, author= "R. J. Lipton and R. E. Tarjan", title= "A separator theorem for planar graphs", journal="SIAM J Appl. Math", annote= "A separator theorem and a linear algorithm for finding the separator are given in the paper.", volume= 36, year= "1979", pages= "177-189") @article(LipTar80, author= "R. J. Lipton and R. E. Tarjan", title= " Applications of a planar sepatator theorem", journal="SIAM J Comput", annote= "Use the planar sepatator theorem to explore sveral problems in planar graph including NP-C problem,Maxium matching , etc", volume= 9, year= "1980", pages= "") @article(Had75, author= "F Hadlock", title= "Finding a maximum cut of a planar graph in polynomial time", journal="SIAM J Comput", annote= "A proof that the maximum cut problem can be translated into a maximum weighted matching problem for which there exists a polynomial bounded algorithm", volume= 4, year= "1975", pages= "221-225") @article(Lub86, author= "M Luby", title= "A simple parallel algorithm for the maximal independent set", journal="SICOMP", annote= "It gives an parallel algorithm for mazimal independent set with $O(log^2n)$ time in $O(n^3)$ processors", volume= 15, year= "1986", pages= "") @inproceedings(HopWon74, author= "J.E. Hopcroft and J.K. Wong", title= "Linear time algorithm for isomorphism of planar graphs ", booktitle="Preceedings of the 6th Annual ACM Symposium on Theory of Computing ", annote= "An O(n) algorithm for testing the isomorphism of planar graphs ", year= "1974", pages= "172--184") @phdthesis(Kar76, author= "O Kariv", title= "An $O(n^2.5)$ algorithm for finding a maximum matching on a general graph", title="Ph.D dissertation Weizmann Institute of Science Rehovot Israel ", annote= "", year= "1976", pages= "") @article(HopTar73, author= "J.E. Hopcroft and R.E. Tarjan", title= "An $O(nlogn)$ algorithm for ismorphism of tri-connected planar graphs", journal="J of Computer and System Science", annote= "", volume= 7, year= "1973", pages= "323--331") @inproceedings(GazRei90, author= "H Gazit and J H. Reif", title= "A randomized paralled algorithm for planar graph isomorphism ", booktitle="In 2nd Annual ACM Symposium on parallel algorithms and architectures", annote= "An algorithm of O({\it log(n)}) with O(\(n^{1.5}\sqrt{\it log(n)}\)) processors for testing planar graph isomorphism", year= "1990", pages= "210--219") @techreport(GazMil91, author= "H Gazit and Gary L. Miller", title= "A deterministic parallel algorithm for finding a sepatator in planar graph ", institution="Technical Rept. CMU-CS-91-103 CMU", annote= "Seperator of a planar graph is useful for many kind of problems in planar graph. The paper gives a deterministic parallel algorithm for finding a sepatator in planar graph", year= "1991", pages= "") @inproceedings(Gaz84, author= "H Gazit", title= "Optimal EREW parallel algorithms for connectivity , ear decomposition and st-numbering of planar graphs", booktitle="In 5th International parallel processing Symposium", annote= "", year= "1984", pages= "84--91") @article(RamRei***, author= "Vijya Ramachandran and J H Reif", title= "An optimal parallel algorithm for graph planarity", journal="", annote= "", volume= "", year= "", pages= "") @inproceedings(DjiPanZar91, author= "H N Djidev and G E Pantziou and C D Zaroliagis", title= "Computing shortest pathes and distances in planar graphs", booktitle="Proc 18 International Colloquium on Automata languages and prograssing", annote= "", year= "1991", pages= "327-338") @article(Lyn75, author= "J F Lynch", title= "The equivalence of theorem proving and the interconnection problem", journal="ACM SIGDA Newsletter", annote= "", volume= 5, year= "1875", pages= "31--65") @inproceedings(SuzYamNis90, author= "H Suzuki and C Yamanaka and T Nishizeki", title= "Parallel algorithms for finding steiner forests in planar graphs", booktitle="Algorithms International Symposium SIGAL '90 Preceedings", annote= " 4 parallel algorithms for finding steiner forests under different conditions in planar graphs", year= "1990", pages= "458--467") @book(GarJoh79, author= "MR Garey and D S Johnson", title="Computers and Intractability: a Guide to the theory of NP Completeness", publisher="", annote= "Introduction of NP problems ", year= "1979",) @article(Bak94, author= "B S Baker", title= "Approximation algorithms for NP-complete problems on planar graphs", journal="Journal of the Association for Computing Machinery", annote= "The paper dscribe a technique to obtain approximation schemas for various NP-complete problem in planar graph . It decomposes a planar graph into subgraphs of a form called k-outer planar graph and combines optimal solution for k-outer planar subgraphs", volume= 41, year= "1994", pages= "153-180") @article(AppHak76, author= "K Apple and W. Haken", title= "Every planar map is four colorable", journal="Bull. Amer. Math. Soc.", annote= "The proof of that every planar graph is four colorable is given.", volume= "82", year= "1976", pages= "711-712") @article(AppHak77, author= "K. Appel and W Haken", title= "Every planar map is 4-colorable", journal="Illinois J. Math", annote= "A proof of that every planar map is 4-colorable, which is a breakthrough in the coloring problem in planar graph.", volume= "21", year= "1977", pages= "429-567") @article(ChiNisSai82, author= "Norishige Chiba and Takao Nishizeki and Nobuji Saito", title= "An approximation algorithm for the maximum independent set problem on planar graph", journal="SIAM J. Comput", annote= "The the maximum independent set problem is NP. An approximation algorithm for the maximum independent set problem on planar graph is given", volume= "4", year= "1982", pages= "663-675") @article(Tuc73, author= "Alan Tucker", title= "The strong perfect graph conjecture for planar graphs", journal="Canad. J. Math.", annote= "I can not find the journal in the libraries that I can access right now.", volume= "25", year= "1973", pages= "103-114") @article(PapYan81, author= "Christos H Papadimitriou and Mihalis Yannakakis", title= "The clique problem for planar graphs", journal="Inform. Process Lett.", annote= "The paper show that a planar graph can not contain a 5-clique. The maximum clique problem can be solved by list all triples and 4-clique. It can be done in O(n) time. ", volume= "13", year= "1981", pages= "131--133") @inproceedings(PanSpiZar90, author= "G. E. Pantziou and P. G. Spirakis and C. D. Zaroliagis", title= "Efficient parallel algorithms for shortest paths in planar graphs", booktitle="SWAT 90. 2nd Scandinavian Workshop on Algorithm theory ", annote= "A parallel algorithm of \((log^{2}n+log^{3}q\)) with O({\it nq}) processors for finding the shortest paths in planar graphs. q is the number of faces that cover all the vertices", year= "1990", pages= "288-300") @incollection(Ling90, author= "A. Lingas", title= "Efficient parallel Algorithms for path problems in planar directed graphs", booktitle="Algorithms, International SIGAL 90", annote= "An algorithm O(\(log^4n)\) with O(\(n^2/log^2n)\) processors for finding all shortest pathes", year= "1990", pages= "447-457") @article(Sto73, author= "L. Stockmeyer", title= "Planar 3-colorability is polynomal complete", journal="SIGACT News", annote= "Proof 3-coloring planar graph is polynomal complete", volume= "5", year= "1973", pages= "19-25") @incollection(MicVaz80, author= "S Micali and V. Vazirani", title= "An O(\(n^{1/2}m\)) algorithm for finding maximum matching in general graphs", booktitle="21th Annual Symp. on Found . of Comp. Sci.", year= "1980", pages= "17-27") @article(, author= "", title= "", journal="", annote= "", volume= "", year= "", pages= "") @article(, author= "", title= "", journal="", annote= "", volume= "", year= "", pages= "") @article(, author= "", title= "", journal="", annote= "", volume= "", year= "", pages= "") @article(, author= "", title= "", journal="", annote= "", volume= "", year= "", pages= "") @article(, author= "", title= "", journal="", annote= "", volume= "", year= "", pages= "") @article(, author= "", title= "", journal="", annote= "", volume= "", year= "", pages= "") @article(, author= "", title= "", journal="", annote= "", volume= "", year= "", pages= "")