On the Structure of Graphs Without Claw, 4K1 and co-R

被引：0

作者：

Abuadas, Tala ^{[1
]}

Hoang, Chinh T. ^{[1
]}

机构：

[1] Wilfrid Laurier Univ, Dept Phys & Comp Sci, Waterloo, ON, Canada

来源：

GRAPHS AND COMBINATORICS | 2022年 / 38卷 / 04期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Graph coloring; Line-graph; Claw; Co-R; Clique width; CLIQUE-WIDTH;

D O I：

10.1007/s00373-022-02517-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a family F of graphs, a graph G is F-free if it does not contain any graph in F as an induced subgraph. The problem of determining the complexity of vertex coloring (claw, 4K(1))-free graphs is a well known open problem. In this paper, we solve the coloring problem for a subclass of (claw, 4K(1))-free graphs. We design a polynomial-time algorithm to color (claw, 4K(1), co-R)-free graphs. This algorithm is derived from a structural theorem on (claw, 4K(1), co-R)-free graphs.

引用

页数：19

共 50 条

[1] On the Structure of Graphs Without Claw, 4K1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4K_1$$\end{document} and co-R
Tala Abuadas
Chính T. Hoàng
Graphs and Combinatorics, 2022, 38 (4)
[2] Coloring (4K1,C4,C6)-free graphs
Penev, Irena
DISCRETE MATHEMATICS, 2023, 346 (11)
[3] Characterizations of (4K1, C4, C5)-free graphs
Fraser, Dallas J.
Hamel, Angele M.
Hoang, Chinh T.
Holmes, Kevin
LaMantia, Tom P.
DISCRETE APPLIED MATHEMATICS, 2017, 231 : 166 - 174
[4] Vertex coloring (4K1, hole-twin, 5-wheel)-free graphs
Dai, Yingjun
Foley, Angele M.
Hoang, Chinh T.
THEORETICAL COMPUTER SCIENCE, 2022, 914 : 14 - 22
[5] Matching extension in K-1,K-r-free graphs with independent claw centers
Ryjacek, Z
DISCRETE MATHEMATICS, 1997, 164 (1-3) : 257 - 263
[6] A Note on Coloring (4K1, C4, C6)-Free Graphs with a C7
Koutecky, Martin
GRAPHS AND COMBINATORICS, 2022, 38 (05)
[7] On the clique-width of (4K1, C4, C5, C7)-free graphs
Penev, Irena
DISCRETE APPLIED MATHEMATICS, 2020, 285 : 688 - 690
[8] Structure of 4-connected claw-free graphs not containing a subdivision of K5
Krakovski, Roi
Stephens, D. Christopher
DISCRETE MATHEMATICS, 2011, 311 (12) : 908 - 910
[9] GRAPHS WITHOUT K(4)-MINORS
LAI, HJ
LAI, HY
ARS COMBINATORIA, 1993, 36 : 327 - 334
[10] On connected [k, k+1]-factors in claw-free graphs
Li, GJ
Zhu, BH
Chen, CP
ARS COMBINATORIA, 2002, 62 : 207 - 219

← 1 2 3 4 5 →