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The competition number of a graph with exactly two holes

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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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Authors and Affiliations

  1. Department of Mathematics, National Taiwan University, Taipei, 10617, Taiwan

    Bo-Jr Li & Gerard J. Chang

  2. Institute for Mathematical Sciences, National Taiwan University, Taipei, 10617, Taiwan

    Gerard J. Chang

  3. National Center for Theoretical Sciences, Taipei Office, Taipei, Taiwan

    Bo-Jr Li & Gerard J. Chang

Authors
  1. Bo-Jr Li
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  2. Gerard J. Chang
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Corresponding author

Correspondence to Gerard J. Chang.

Additional information

Supported in part by the National Science Council under grant NSC95-2115-M-002-0013-MY3.

This paper is a revision of Chap. 6 in the first author’s Doctoral Dissertation.

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Li, BJ., Chang, G.J. The competition number of a graph with exactly two holes. J Comb Optim 23, 1–8 (2012). https://doi.org/10.1007/s10878-010-9331-9

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  • DOI: https://doi.org/10.1007/s10878-010-9331-9

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