Coloring Plane Graphs with Independent Crossings

被引：38
|
作者：
Kral, Daniel [1 ]
Stacho, Ladislav [2 ]
机构：
[1] Charles Univ Prague, Fac Math & Phys, Inst Theoret Comp Sci ITI, Prague 11800, Czech Republic
[2] Simon Fraser Univ, Dept Math, Burnaby, BC V5A 1S6, Canada
来源：
JOURNAL OF GRAPH THEORY | 2010年 / 64卷 / 03期
基金：
加拿大自然科学与工程研究理事会;
关键词：
planar graphs; cyclic coloring; crossing number; chromatic number; CYCLIC COLORINGS; FACIAL COLORINGS; THEOREM;
D O I：
10.1002/jgt.20448
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that every plane graph with maximum face size four in which all faces of size four are vertex-disjoint is cyclically 5-colorable. This answers a question of Albertson whether graphs drawn in the plane with all crossings independent are 5-colorable. (C) 2009 Wiley Periodicals, Inc. J Graph Theory 64: 184-205. 2010
引用
收藏
页码：184 / 205
页数：22
相关论文
共 50 条
  • [1] The structure of plane graphs with independent crossings and its applications to coloring problems
    Zhang, Xin
    Liu, Guizhen
    CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2013, 11 (02): : 308 - 321
  • [2] Strong Edge Coloring of Outerplane Graphs with Independent Crossings
    Li, Ke-Jie
    Zhang, Xin
    ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2024, 40 (02): : 467 - 477
  • [3] Strong Edge Coloring of Outerplane Graphs with Independent Crossings
    Ke-Jie LI
    Xin ZHANG
    Acta Mathematicae Applicatae Sinica, 2024, 40 (02) : 467 - 477
  • [4] Coloring graphs with crossings
    Oporowski, Bogdan
    Zhao, David
    DISCRETE MATHEMATICS, 2009, 309 (09) : 2948 - 2951
  • [5] Light triangles in plane graphs with near-independent crossings
    Tian, Jingjing
    Zhang, Xin
    UTILITAS MATHEMATICA, 2015, 97 : 399 - 405
  • [6] Equitable partition of plane graphs with independent crossings into induced forests
    Niu, Bei
    Zhang, Xin
    Gao, Yuping
    DISCRETE MATHEMATICS, 2020, 343 (05)
  • [7] On (p, 1)-total labelling of plane graphs with independent crossings
    Zhang, Xin
    Liu, Guizhen
    Yu, Yong
    FILOMAT, 2012, 26 (06) : 1091 - 1100
  • [8] Total coloring of outer-1-planar graphs with near-independent crossings
    Xin Zhang
    Journal of Combinatorial Optimization, 2017, 34 : 661 - 675
  • [9] Total coloring of outer-1-planar graphs with near-independent crossings
    Zhang, Xin
    JOURNAL OF COMBINATORIAL OPTIMIZATION, 2017, 34 (03) : 661 - 675
  • [10] 5-COLORING GRAPHS WITH 4 CROSSINGS
    Erman, Rok
    Havet, Frederic
    Lidicky, Bernard
    Pangrac, Ondrej
    SIAM JOURNAL ON DISCRETE MATHEMATICS, 2011, 25 (01) : 401 - 422
12345