Graphs with no induced five-vertex path or antipath
  We prove that a graph $G$ contains no induced $5$-vertex path and no induced complement of a $5$-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. 
Maria Chudnovsky, Louis Esperet, Laetitia Lemoine, Peter Maceli,   Fr\'ed\'eric Maffray, and Irena Penev
math.CO cs.DM