Graphs with No Induced Five-Vertex Path or Antipath

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

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 (US)
Pages (from-to)221-232
Number of pages12
JournalJournal of Graph Theory
Issue number3
StatePublished - Mar 1 2017

All Science Journal Classification (ASJC) codes

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


  • P5
  • decomposition
  • forbidden subgraph


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