Forbidden induced subgraphs for star-free graphs

Jun Fujisawa, Katsuhiro Ota, Kenta Ozeki, Gabriel Sueiro

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Let H be a family of connected graphs. A graph G is said to be H-free if G is H-free for every graph H in H. In Aldred et al. (2010) [1], it was pointed that there is a family of connected graphs H not containing any induced subgraph of the claw having the property that the set of H-free connected graphs containing a claw is finite, provided also that those graphs have minimum degree at least 2 and maximum degree at least 3. In the same work, it was also asked whether there are other families with the same property. In this paper, we answer this question by solving a wider problem. We consider not only claw-free graphs but the more general class of star-free graphs. Concretely, given t<3, we characterize all the graph families H such that every large enough H-free connected graph is K1,t-free. Additionally, for the case t=3, we show the families that one gets when adding the condition |H|≤k for each positive integer k.

Original languageEnglish
Pages (from-to)2475-2484
Number of pages10
JournalDiscrete Mathematics
Volume311
Issue number21
DOIs
Publication statusPublished - 2011 Nov 6

Keywords

  • Claw-free
  • Forbidden subgraph
  • Star-free

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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