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
  • [21] On Choosability with Separation of Planar Graphs with Forbidden Cycles
    Choi, Ilkyoo
    Lidicky, Bernard
    Stolee, Derrick
    JOURNAL OF GRAPH THEORY, 2016, 81 (03) : 283 - 306
  • [22] On 3-choosability of plane graphs without 6-, 7-and 9-cycles
    Zhang H.
    Xu B.
    Applied Mathematics-A Journal of Chinese Universities, 2004, 19 (1) : 109 - 115
  • [23] On acyclic 4-choosability of planar graphs without short cycles
    Chen, Min
    Raspaud, Andre
    DISCRETE MATHEMATICS, 2010, 310 (15-16) : 2113 - 2118
  • [24] Acyclic 4-Choosability of Planar Graphs Without 4-Cycles
    Yingcai Sun
    Min Chen
    Czechoslovak Mathematical Journal, 2020, 70 : 161 - 178
  • [25] Acyclic 4-Choosability of Planar Graphs Without 4-Cycles
    Sun, Yingcai
    Chen, Min
    CZECHOSLOVAK MATHEMATICAL JOURNAL, 2020, 70 (01) : 161 - 178
  • [26] Choosability with union separation of planar graphs without cycles of length 4
    Hou, Jianfeng
    Zhu, Hongguo
    APPLIED MATHEMATICS AND COMPUTATION, 2020, 386
  • [27] 5-choosability of graphs with. crossings far apart
    Dvorak, Zdenek
    Lidicky, Bernard
    Mohar, Bojan
    JOURNAL OF COMBINATORIAL THEORY SERIES B, 2017, 123 : 54 - 96
  • [28] Acyclic 3-choosability of sparse graphs with girth at least 7
    Borodin, O. V.
    Chen, M.
    Ivanova, A. O.
    Raspaud, A.
    DISCRETE MATHEMATICS, 2010, 310 (17-18) : 2426 - 2434
  • [29] Edge choosability of planar graphs without small cycles
    Zhang, L
    Wu, BYD
    DISCRETE MATHEMATICS, 2004, 283 (1-3) : 289 - 293
  • [30] Choosability with separation of planar graphs without prescribed cycles
    Chen, Min
    Fan, Yingying
    Raspaud, Andre
    Shiu, Wai Chee
    Wang, Weifan
    APPLIED MATHEMATICS AND COMPUTATION, 2020, 367
12345