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The competition number of a graph with?exactly?two?holes
Authors:Bo-Jr Li  Gerard J Chang
Institution:1. Department of Mathematics, National Taiwan University, Taipei, 10617, Taiwan
3. National Center for Theoretical Sciences, Taipei Office, Taipei, Taiwan
2. Institute for Mathematical Sciences, National Taiwan University, Taipei, 10617, Taiwan
Abstract:Given an acyclic digraph D, the competition graph C(D) of 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 v in D such that (x,v) and (y,v) are arcs of D. The competition number κ(G) of a graph G is the least number of isolated vertices that must be added to G to form a competition graph. The purpose of this paper is to prove that the competition number of a graph with exactly two holes is at most three.
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