Competition numbers of complete r-partite graphs

被引：9
|
作者：
Li, Bo-Jr [2 ]
Chang, Gerard J. [1 ,3 ,4 ]
机构：
[1] Natl Taiwan Univ, Dept Math, Taipei 10617, Taiwan
[2] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 80424, Taiwan
[3] Natl Taiwan Univ, Taida Inst Math Sci, Taipei 10617, Taiwan
[4] Natl Ctr Theoret Sci, Taipei Off, Taipei, Taiwan
来源：
DISCRETE APPLIED MATHEMATICS | 2012年 / 160卷 / 15期
关键词：
Competition graph; Competition number; Complete r-partite graph; Latin square; HAMMING GRAPHS;
D O I：
10.1016/j.dam.2012.05.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The competition graph C(D) of an acyclic digraph D is the graph with the same vertex set as D and two distinct vertices x and y are adjacent in C(D) if and only if there is a vertex upsilon in D such that (x, upsilon) and (y, upsilon) are arcs of D. The competition number kappa(G) of a graph G is the minimum number of isolated vertices that must be added to G to form the competition graph of an acyclic digraph. In this paper, we investigate competition numbers of complete r-partite graphs K-n1,K- n2,K- . . . ,K- (nr) In particular, we determine the numbers for r = 3 and for some cases of r >= 4. We also give bounds for the competition numbers of general complete r-partite graphs. (C) 2012 Elsevier B.V. All rights reserved.
引用
收藏
页码：2271 / 2276
页数：6
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