Perfection of glued graphs of perfect original graphs

Abstract

A graph G is perfect if the chromatic number and the clique number have the same value for every of its induced subgraph. A glued graph results from combining two vertex-disjoint graphs by identifying nontrivial connected isomorphic subgraphs of both graphs. Such subgraphs are referred to as the clones. The two vertex-disjoint graphs are referred to the original graphs. The main results involve in the perfection of glued graphs whose original graphs are perfect. We find necessary and/or sufficient conditions for the perfections of glued graphs. We also study the chromatic number and the clique numbers of glued graphs in terms of these parameters of their original graphs. Only some specified clones and original graphs are investigated:- clones such as induced subgraphs of both original graphs and complete graphs; original graphs such as bipartite graphs, complete graphs and forests.