The Chromatic Number of a Graph with Two Odd Holes and an Odd Girth

被引：0
|
作者：
Lan, Kaiyang [1 ]
Liu, Feng [2 ]
机构：
[1] Fuzhou Univ, Ctr Discrete Math, Fujian 350003, Peoples R China
[2] East China Normal Univ, Dept Math, Shanghai 200241, Peoples R China
来源：
GRAPHS AND COMBINATORICS | 2023年 / 39卷 / 06期
关键词：
Chromatic number; Girth; Odd hole;
D O I：
10.1007/s00373-023-02723-y
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
An odd hole is an induced odd cycle of length at least five. Let l >= 2 be an integer, and let G(l) denote the family of graphs which have girth 2l + 1 and have no holes of odd length at least 2l + 5. In this paper, we prove that every graph G is an element of U(l >= 3)G(l) is 4-colourable.
引用
下载
收藏
页数：6
相关论文
共 50 条
  • [1] The Chromatic Number of a Graph with Two Odd Holes and an Odd Girth
    Kaiyang Lan
    Feng Liu
    Graphs and Combinatorics, 2023, 39
  • [2] On the chromatic number of graphs of odd girth without longer odd holes
    Wang, Hongyang
    DISCRETE APPLIED MATHEMATICS, 2024, 342 : 227 - 230
  • [3] Odd Chromatic Number of Graph Classes
    Belmonte, Remy
    Harutyunyan, Ararat
    Kohler, Noleen
    Melissinos, Nikolaos
    GRAPH-THEORETIC CONCEPTS IN COMPUTER SCIENCE, WG 2023, 2023, 14093 : 44 - 58
  • [4] On the odd girth and the circular chromatic number of generalized Petersen graphs
    Amir Daneshgar
    Meysam Madani
    Journal of Combinatorial Optimization, 2017, 33 : 897 - 923
  • [5] On the odd girth and the circular chromatic number of generalized Petersen graphs
    Daneshgar, Amir
    Madani, Meysam
    JOURNAL OF COMBINATORIAL OPTIMIZATION, 2017, 33 (03) : 897 - 923
  • [6] The Odd Chromatic Number of a Planar Graph is at Most 8
    Petr, Jan
    Portier, Julien
    GRAPHS AND COMBINATORICS, 2023, 39 (02)
  • [7] The odd chromatic number of a toroidal graph is at most 9
    Tian, Fangyu
    Yin, Yuxue
    INFORMATION PROCESSING LETTERS, 2023, 182
  • [8] The Odd Chromatic Number of a Planar Graph is at Most 8
    Jan Petr
    Julien Portier
    Graphs and Combinatorics, 2023, 39
  • [9] The circular chromatic number of series-parallel graphs of large odd girth
    Pan, ZS
    Zhu, XD
    DISCRETE MATHEMATICS, 2002, 245 (1-3) : 235 - 246
  • [10] The odd girth of the generalised Kneser graph
    Denley, T
    EUROPEAN JOURNAL OF COMBINATORICS, 1997, 18 (06) : 607 - 611
12345