It is well-known that the GRAPH 3.COLORABILITY problem, deciding whether a given graph has a stable set whose deletion results in a bipartite graph, is NP-complete. We prove the following relatedâ€¦ (More)

We answer a question of Corneil and Fonlupt by showing that deciding whether a graph has a stable cutset is NP-complete even for restricted graph classes. Some e ciently solvable cases will beâ€¦ (More)

A graph is a homogeneous extension of a tree iff the reduction of all hom ogeneous sets (sometimes called modules) to single vertices gives a tree. We show that these graphs can be recognized inâ€¦ (More)

In this paper, we consider the râ€“dominating set problem on graphs which can be generated from the one-vertex graph by a finite number of homogeneous extensions and by attaching pendant vertices. Weâ€¦ (More)

Using the idea due to P. D UCHET in proving his wellâ€“known theorem on powers of chordal graphs, we shall describe some theorems of D UCHETâ€“type for powers of graphs that have no long induced cycles.â€¦ (More)