INTERVAL EDGE-COLORING OF COMPLETE AND COMPLETE BIPARTITE GRAPHS WITH RESTRICTIONS

Abstract

An edge-coloring of a graph G with consecutive integers c1,…,ct is called an interval t-coloring, if all colors are used, and the colors of edges incident to any vertex of G are distinct and form an interval of integers. A graph G is interval colorable if it has an interval t-coloring for some positive integer t. In this paper, we consider the case where there are restrictions on the edges, and the edge-coloring should satisfy these restrictions. We show that the problem is NP-complete for complete and complete bipartite graphs. We also provide a polynomial solution for a subclass of complete bipartite graphs when the restrictions are on the vertices.