The competition number of a graph with exactly two holes

Bo-Jr Li and Gerard J. Chang ()
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Bo-Jr Li: National Taiwan University
Gerard J. Chang: National Taiwan University

Journal of Combinatorial Optimization, 2012, vol. 23, issue 1, No 1, 8 pages

Abstract: 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.

Keywords: Competition graph; Competition number; Chordal graph; Chordless cycle; Hole (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10878-010-9331-9

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