Convex hull of the edges of a graph and near bipartite graphs

AbstractFirst we characterize the convex hull of the edges of a graph, edges viewed as the characteristic function of the hereditary closure of some subset of the 2-elements set of a finite set X. This characterization becomes more simple for a class of graphs that we call near bipartite, NBP in short. This class is then characterized as the class of graphs such that ∀xϵX, GX\r(x), the induced subgraph of the complementary of the neighbourhood of x, is bipartite. We made a partial study of this class, whose interest is justified by the constatation that the following classes are strictly include: L(G) the edge complementary of the line graph of G. NBP, K13-free graphs