Simplicial vertices in graphs with no induced four-edge path or four-edge antipath, and the H6-conjecture

Maria Chudnovsky, Peter MacEli

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let G be the class of all graphs with no induced four-edge path or four-edge antipath. Hayward and Nastos conjectured that every prime graph in G not isomorphic to the cycle of length five is either a split graph or contains a certain useful arrangement of simplicial and antisimplicial vertices. In this article, we give a counterexample to their conjecture, and prove a slightly weaker version. Additionally, applying a result of the first author and Seymour we give a short proof of Fouquet's result on the structure of the subclass of bull-free graphs contained in G.

Original languageEnglish (US)
Pages (from-to)249-261
Number of pages13
JournalJournal of Graph Theory
Volume76
Issue number4
DOIs
StatePublished - Aug 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Keywords

  • antipath
  • induced subgraph
  • path

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