Let (P,≺) be a finite poset and let G be its comparability graph. If cl(G) is the clutter of maximal cliques of G, we prove that cl(G) satisfies the maxflow min-cut property and that its edge ideal is normally torsion free. We prove that edge ideals of complete admissible uniform clutters are normally torsion free. The normality of a monomial ideal is expressed in terms of blocking polyhedra an...

We study the neighborhood polynomial and complexity of its computation for chordal graphs. The a graph is generating function subsets vertices that have common neighbor. introduce parameter graphs called anchor width an algorithm to compute which runs in time if polynomially bounded. maximal number different sub-cliques clique appear as neighborhood. Furthermore we some subclasses such comparab...

We characterize even and odd pairs in comparability and in P 4-comparability graphs. The characterizations lead to simple algorithms for deciding whether a given pair of vertices forms an even or odd pair in these classes of graphs. The complexities of the proposed algorithms are O(n + m) for comparability graphs and O(n 2 m) for P 4-comparability graphs. The former represents an improvement ov...