The competition number of a graph with exactly h holes, all of which are independent

Authors:
Bo-Jr Li;Gerard J. Chang
Affiliations:
Department of Mathematics, National Taiwan University, Taipei 10617, Taiwan;Department of Mathematics, National Taiwan University, Taipei 10617, Taiwan and Institute for Mathematical Sciences, National Taiwan University, Taipei 10617, Taiwan and National Center for Theore ...
Venue:
Discrete Applied Mathematics
Year:
2009

Citing 4
Cited 4

The competition-common enemy graph of a digraph

Discrete Applied Mathematics
Niche graphs

Discrete Applied Mathematics
Niche numbers

Journal of Graph Theory
Competition numbers of graphs with a small number of triangles

Discrete Applied Mathematics

Note: An upper bound for the competition numbers of graphs

Discrete Applied Mathematics
Note: The competition number of a graph whose holes do not overlap much

Discrete Applied Mathematics
The competition number of a graph with exactly two holes

Journal of Combinatorial Optimization
Competition numbers of complete r-partite graphs

Discrete Applied Mathematics

Quantified Score

Hi-index	0.04

Visualization

Abstract

Given an acyclic digraph D, the competition graph C(D) of D is the graph with the same vertex set as D where 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 @k(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 h holes, all of which are independent, is at most h+1. This generalizes the result for h=0 given by Roberts, and the result for h=1 given by Cho and Kim.