Given a graph (directed or undirected) with costs on the edges, and an integer k, we consider the problem of nding a k-node connected spanning subgraph of minimum cost. For the ge...
Given a graph on n vertices which is the union of two comparability graphs on the same vertex set, it always contains a clique or independent set of size n 1 3 . On the other hand...
An edge-labeling λ for a directed graph G has a weak sense of direction (WSD) if there is a function f that satisfies the condition that for any node u and for any two label seq...
In social network theory, a simple graph G is called k-role assignable if there is a surjective mapping that assigns a number from {1, . . . , k} called a role to each vertex of G ...
Let K− r denote the graph obtained from Kr by deleting one edge. We show that for every integer r ≥ 4 there exists an integer n0 = n0(r) such that every graph G whose order n ...