Title
Transversals and competition numbers of complete multipartite graphs.
Abstract
Let G denote a simple graph and let Ik denote the graph on k isolated vertices. The competition number of G is the minimum integer k such that G∪Ik is the competition graph of an acyclic digraph. We show that if n≥5 is odd, then the competition number of the complete tetrapartite graph Kn4 is at most n2−4n+8. We also show that if n is a prime integer and m≤n, then the competition number of Knm is at most n2−2n+3.
Year
DOI
Venue
2013
10.1016/j.dam.2012.09.012
Discrete Applied Mathematics
Keywords
Field
DocType
Competition acyclic digraph latin square transversal multipartite complete graph
Discrete mathematics,Combinatorics,Graph toughness,Graph power,Cycle graph,Regular graph,Null graph,Distance-regular graph,Windmill graph,Mathematics,Complement graph
Journal
Volume
Issue
ISSN
161
3
0166-218X
Citations 
PageRank 
References 
4
0.44
6
Authors
1
Name
Order
Citations
PageRank
Jaromy Kuhl1104.72