Transformations which Preserve Perfectness and H-Perfectness of Graphs

A graph G is h-perfect if the convex hull of the incidence vectors of the independent sets of G is a polytope defined by nonnegativity constraints, clique constraints and odd holes constraints. We prove the two following theorems: (1) A graph obtained by identification of two vertices of a bipartite graph is h-perfect. (2) If in a perfect graph there exists two vertices b and c such that all the minimal chains between b and c have an odd number of vertices, the graph obtained by identification of b and c is perfect.