On clique coverings of complete multipartite graphs

被引：0
|
作者：
Davoodi, Akbar [1 ]
Gerbner, Daniel [2 ]
Methuku, Abhishek [3 ]
Vizer, Mate [2 ]
机构：
[1] Inst Res Fundamental Sci IPM, Sch Math, POB 19395-5746, Tehran, Iran
[2] MTA Alfred Renyi Inst Math, Budapest, Hungary
[3] Ecole Polytech Fed Lausanne, Lausanne, Switzerland
来源：
DISCRETE APPLIED MATHEMATICS | 2020年 / 276卷
关键词：
Clique covering; Sigma clique covering; Qualitatively independent family;
D O I：
10.1016/j.dam.2019.09.014
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A clique covering of a graph G is a set of cliques of G such that any edge of G is contained in one of these cliques, and the weight of a clique covering is the sum of the sizes of the cliques in it. The sigma clique cover number scc(G) of a graph G, is defined as the smallest possible weight of a clique covering of G. Let K-t(d) denote the complete t-partite graph with each part of size d. We prove that for any fixed d >= 2, we have lim(t ->infinity) scc(K-t(d)) = d/2t log t. This disproves a conjecture of Davoodi et al. (2016). (C) 2019 Elsevier B.V. All rights reserved.
引用
收藏
页码：19 / 23
页数：5
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