Open AccessThe competition number of a graph with exactly two holes
Author(s) -
Bo-Jr Li,
Gerard J. Chang
Publication year - 2010
Publication title -
journal of combinatorial optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.538
H-Index - 48
eISSN - 1573-2886
pISSN - 1382-6905
DOI - 10.1007/s10878-010-9331-9
Subject(s) - combinatorics , mathematics , vertex (graph theory) , graph , discrete mathematics , neighbourhood (mathematics) , regular graph , complement graph , digraph , graph power , line graph , mathematical analysis
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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