Three new upper bounds on the chromatic number

被引：4

作者：

Soto, Maria ^{[1
]}

Rossi, Andre ^{[1
]}

Sevaux, Marc ^{[1
]}

机构：

[1] Univ Bretagne Sud, CNRS, UMR 3192, Ctr Rech,Lab STICC, F-56321 Lorient, France

来源：

DISCRETE APPLIED MATHEMATICS | 2011年 / 159卷 / 18期

关键词：

Graph coloring; Chromatic number; Upper bounding scheme; COLORING GRAPHS; ALGORITHM;

D O I：

10.1016/j.dam.2011.08.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper introduces three new upper bounds on the chromatic number, without making any assumptions on the graph structure. The first one xi, is based on the number of edges and nodes, and is to be applied to any connected component of the graph, whereas zeta and eta are based on the degree of the nodes in the graph. The computation complexity of the three-bound computation is assessed. Theoretical and computational comparisons are also made with five well-known bounds from the literature, which demonstrate the superiority of the new upper bounds. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：2281 / 2289

页数：9

共 50 条

[21] A new upper bound on the cyclic chromatic number
Borodin, O. V.
Broersma, H. J.
Glebov, A.
van den Heuvel, J.
JOURNAL OF GRAPH THEORY, 2007, 54 (01) : 58 - 72
[22] A NEW UPPER BOUND FOR THE LIST CHROMATIC NUMBER
BOLLOBAS, B
HIND, HR
DISCRETE MATHEMATICS, 1989, 74 (1-2) : 65 - 75
[23] A new upper bound for the harmonious chromatic number
Edwards, K
JOURNAL OF GRAPH THEORY, 1998, 29 (04) : 257 - 261
[24] Algorithmic bounds for the chromatic number
Schiermeyer, Ingo
OPTIMIZATION, 2008, 57 (01) : 153 - 158
[25] Bounds on the Distinguishing Chromatic Number
Collins, Karen L.
Hovey, Mark
Trenk, Ann N.
ELECTRONIC JOURNAL OF COMBINATORICS, 2009, 16 (01):
[26] Bounds on the Dynamic Chromatic Number of a Graph in Terms of its Chromatic Number
Vlasova N.Y.
Karpov D.V.
Journal of Mathematical Sciences, 2018, 232 (1) : 21 - 24
[27] Upper bounds on the chromatic number of triangle-free graphs with a forbidden subtree
Xiao Wang
Baoyindureng Wu
Journal of Combinatorial Optimization, 2017, 33 : 28 - 34
[28] Upper bounds on the chromatic number of triangle-free graphs with a forbidden subtree
Wang, Xiao
Wu, Baoyindureng
JOURNAL OF COMBINATORIAL OPTIMIZATION, 2017, 33 (01) : 28 - 34
[29] New bounds for the chromatic number of a space with forbidden isosceles triangles
Samirov, D. V.
Raigorodskii, A. M.
DOKLADY MATHEMATICS, 2014, 89 (03) : 313 - 316
[30] New bounds for the chromatic number of a space with forbidden isosceles triangles
D. V. Samirov
A. M. Raigorodskii
Doklady Mathematics, 2014, 89 : 313 - 316

← 1 2 3 4 5 →