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.
All Science Journal Classification (ASJC) codes
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- forbidden subgraph