A polytope P is a model for a combinatorial problem on finite graphs G whose variables are indexed by the edge set E of G if the points of P with (0,1)-coordinates are precisely the characteristic vectors of the subset of edges inducing the feasible configurations for the problem. In the case of the (simple) MaxCut Problem, which is the one that concern us here, the feasible subsets of edges ar...

Given a finite connected bipartite graph B = (X, Y ) we consider the simplicial complexes of complete subgraphs of the square B of B and of its induced subgraphs B[X] and B[Y ]. We prove that these three complexes have isomorphic fundamental groups. Among other applications, we conclude that the fundamental group of the complex of complete subgraphs of a graph G is isomorphic to that of the cli...

It is known that the bandwidth problem is NP-complete for chordal bipartite graphs, while the problem can be solved in polynomial time for bipartite permutation graphs, which is a subclass of chordal bipartite graphs. This paper shows that the problem is NP-complete even for convex bipartite graphs, a subclass of chordal bipartite graphs and a superclass of bipartite permutation graphs. We prov...