Compositions for perfect graphs (Q2266722)

In this paper we introduce a new graph composition, called 2-amalgam, and we prove that the 2-amalgam of perfect graphs is perfect. This composition generalizes many of the operations known to preserve perfection, such as the clique identification, substitution, join and amalgam operations. We give polynomial-time algorithms to determine whether a general graph is decomposable with respect to the 2-amalgam or amalgam operations.