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Graphs with No Induced Five‐Vertex Path or Antipath

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.