3-choosability of planar graphs with (≤4)-cycles far apart

被引：7
|
作者：
Dvorak, Zdenek [1 ]
机构：
[1] Charles Univ Prague, Dept Appl Math, Fac Math & Phys, CR-11800 Prague, Czech Republic
来源：
JOURNAL OF COMBINATORIAL THEORY SERIES B | 2014年 / 104卷
关键词：
Planar graphs; List coloring; LIST COLORINGS; GIRTH-5; MAP;
D O I：
10.1016/j.jctb.2013.10.004
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A graph is k-choosable if it can be colored whenever every vertex has a list of at least k available colors. We prove that if cycles of length at most four in a planar graph G are pairwise far apart, then G is 3-choosable. This is analogous to the problem of Havel regarding 3-colorability of planar graphs with triangles far apart. (C) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码：28 / 59
页数：32
相关论文
共 50 条
  • [31] Edge choosability of planar graphs without short cycles
    Wang, WF
    SCIENCE IN CHINA SERIES A-MATHEMATICS, 2005, 48 (11): : 1531 - 1544
  • [32] Edge choosability of planar graphs without short cycles
    WANG Weifan School of Mathematics and Physics
    Science China Mathematics, 2005, (11) : 1531 - 1544
  • [33] Edge choosability of planar graphs without short cycles
    WANG Weifan School of Mathematics and Physics Zhejiang Normal University Jinhua China
    ScienceinChina,SerA., 2005, Ser.A.2005 (11) : 1531 - 1544
  • [34] Acyclic 4-choosability of planar graphs without intersecting short cycles
    Sun, Yingcai
    Chen, Min
    Chen, Dong
    DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2018, 10 (01)
  • [35] Adaptable choosability of planar graphs with sparse short cycles
    Guan, Albert
    Zhu, Xuding
    DISCRETE MATHEMATICS, 2009, 309 (20) : 6044 - 6047
  • [36] Edge choosability of planar graphs without short cycles
    Weifan Wang
    Science in China Series A: Mathematics, 2005, 48 : 1531 - 1544
  • [37] Structural properties and edge choosability of planar graphs without 4-cycles
    Shen, Yufa
    Zheng, Guoping
    He, Wenjie
    Zhao, Yongqiang
    DISCRETE MATHEMATICS, 2008, 308 (23) : 5789 - 5794
  • [38] Acyclic 5-choosability of planar graphs without 4-cycles
    Borodin O.V.
    Ivanova A.O.
    Siberian Mathematical Journal, 2011, 52 (3) : 411 - 425
  • [39] ACYCLIC 5-CHOOSABILITY OF PLANAR GRAPHS WITHOUT 4-CYCLES
    Borodin, O. V.
    Ivanova, A. O.
    SIBERIAN MATHEMATICAL JOURNAL, 2011, 52 (03) : 411 - 425
  • [40] Acyclic 4-Choosability of Planar Graphs with No 4- and 5-Cycles
    Borodin, Oleg V.
    Ivanova, Anna O.
    JOURNAL OF GRAPH THEORY, 2013, 72 (04) : 374 - 397
12345