Planar Graphs without 7-Cycles Are 4-Choosable

Abstract

Previous article Next article Planar Graphs without 7-Cycles Are 4-ChoosableBabak FarzadBabak Farzadhttps://doi.org/10.1137/05064477XPDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractIn this paper, we show that every planar graph without 7-cycles is 4-choosable.[1] S. Choudum, Some 4-valent, 3-connected, planar, almost pancyclic graphs, Discrete Math., 18 (1977), pp. 125–129. DSMHA4 0012-365X CrossrefISIGoogle Scholar[2] G. Fijavz, , M. Juvan, , B. Mohar and , and R. Skrekovski, Planar graphs without cycles of specific lengths, European J. Combin., 23 (2002), pp. 377–388. EJOCDI 0195-6698 CrossrefISIGoogle Scholar[3] S. Gutner, The complexity of planar graph choosability, Discrete Math., 159 (1996), pp. 119–130. DSMHA4 0012-365X CrossrefISIGoogle Scholar[4] P. Lam, , W. Shiu and , and B. Xu, On structure of some plane graphs with application to choosability, J. Combin. Theory Ser. B, 82 (2001), pp. 285–296. 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AMLEEL 0893-9659 CrossrefISIGoogle ScholarKeywordsplanar graphscoloringchoosability Previous article Next article FiguresRelatedReferencesCited byDetails A sufficient condition for planar graphs to be DP -4-colorable7 October 2022 | Quaestiones Mathematicae, Vol. 5 Cross Ref Two sufficient conditions for a planar graph to be list vertex-2-arborableDiscrete Mathematics, Vol. 345, No. 6 Cross Ref Cover and variable degeneracyDiscrete Mathematics, Vol. 345, No. 4 Cross Ref DP-4-coloring of planar graphs with some restrictions on cyclesDiscrete Mathematics, Vol. 344, No. 11 Cross Ref DP-coloring on planar graphs without given adjacent short cycles10 October 2020 | Discrete Mathematics, Algorithms and Applications, Vol. 13, No. 02 Cross Ref Planar Graphs Without Pairwise Adjacent $3$-, $4$-, $5$-, and $6$-cycle are $4$-choosableTaiwanese Journal of Mathematics, Vol. -1, No. -1 Cross Ref Planar graphs without 7-cycles and butterflies are DP-4-colorableDiscrete Mathematics, Vol. 343, No. 8 Cross Ref DP-4-colorability of planar graphs without adjacent cycles of given lengthDiscrete Applied Mathematics, Vol. 277 Cross Ref List coloring and diagonal coloring for plane graphs of diameter twoApplied Mathematics and Computation, Vol. 363 Cross Ref Facial Colorings of Plane Graphs28 April 2019 | Journal of Interconnection Networks, Vol. 19, No. 01 Cross Ref Planar graphs without chordal 6-cycles are 4-choosableDiscrete Applied Mathematics, Vol. 244 Cross Ref Planar graphs without intersecting 5 -cycles are 4 -choosableDiscrete Mathematics, Vol. 340, No. 8 Cross Ref (4, 2)-Choosability of Planar Graphs with Forbidden Structures14 June 2017 | Graphs and Combinatorics, Vol. 33, No. 4 Cross Ref A sufficient condition for a planar graph to be 4 -choosableDiscrete Applied Mathematics, Vol. 224 Cross Ref Toroidal graphs containing neither K5− nor 6-cycles are 4-choosable26 May 2016 | Journal of Graph Theory, Vol. 85, No. 1 Cross Ref Planar graphs without 4-cycles adjacent to triangles are 4-choosableDiscrete Mathematics, Vol. 339, No. 12 Cross Ref A Note on 3-choosability of Planar Graphs Related to Montanssier’s Conjecture20 November 2018 | Canadian Mathematical Bulletin, Vol. 59, No. 2 Cross Ref Improper Choosability of Planar Graphs without 4-CyclesYingqian Wang and Lingji Xu5 December 2013 | SIAM Journal on Discrete Mathematics, Vol. 27, No. 4AbstractPDF (192 KB)On Coloring Problems26 July 2013 Cross Ref On the vertex-arboricity of planar graphs without 7-cyclesDiscrete Mathematics, Vol. 312, No. 15 Cross Ref Choosability of toroidal graphs without short cyclesJournal of Graph Theory, Vol. 28 Cross Ref Volume 23, Issue 3| 2009SIAM Journal on Discrete Mathematics History Submitted:29 November 2005Accepted:06 April 2009Published online:15 July 2009 InformationCopyright © 2009 Society for Industrial and Applied MathematicsKeywordsplanar graphscoloringchoosabilityMSC codes05C1505C10PDF Download Article & Publication DataArticle DOI:10.1137/05064477XArticle page range:pp. 1179-1199ISSN (print):0895-4801ISSN (online):1095-7146Publisher:Society for Industrial and Applied Mathematics