The fractional chromatic number, the Hall ratio, and the lexicographic product

被引：4
|
作者：
Johnson, P. D., Jr. [1 ]
机构：
[1] Auburn Univ, Dept Math & Stat, Auburn, AL 36849 USA
来源：
DISCRETE MATHEMATICS | 2009年 / 309卷 / 14期
关键词：
Fractional chromatic number; Hall ratio; Lexicographic product; GRAPH;
D O I：
10.1016/j.disc.2008.05.049
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let x(f) denote the fractional chromatic number and p the Hall ratio, and let the lexicographic product of G and H be denoted GlexH. Main results: (i) rho(GlexH) <= chi(f) (G)rho(H); (ii) if rho(G) = chi(f) (G) then rho(GlexH) = rho(G)rho(H) for all H; (iii) chi(f) - rho is unbounded. In addition, the question of how big chi(f)/rho can be is discussed. (C) 2008 Elsevier B.V. All rights reserved.
引用
收藏
页码：4746 / 4749
页数：4
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