Graphs with No Induced Five-Vertex Path or Antipath

Maria Chudnovsky, Louis Esperet, Laetitia Lemoine, Peter Maceli, Frédéric Maffray, Irena Penev

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We prove that a graph G contains no induced five-vertex path and no induced complement of a five-vertex path if and only if G is obtained from 5-cycles and split graphs by repeatedly applying the following operations: substitution, split unification, and split unification in the complement, where split unification is a new class-preserving operation introduced here.
Original languageEnglish
JournalJournal of Graph Theory
Issue number3
Pages (from-to)221–232
Publication statusPublished - 2017

Bibliographical note

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  • Forbidden subgraph
  • P5
  • Decomposition

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