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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.

Graphs with No Induced Five‐Vertex Path or Antipath