A graph G is said to be well-covered if every maximal independent set of vertices has the same cardinality. A planar (simple) graph in which each face is a triangle is called a triangulation. It was proved in an earlier paper [A. Finbow, B. Hartnell, R. Nowakowski, M. Plummer, On well-covered triangulations: Part I, Discrete Appl. Math., 132, 2004, 97–108] that there are no 5-connected planar w...

A graph with n vertices is well-covered if every maximal independent set is a maximum independent set, and very well-covered if every maximal independent set has size n ⁄2. In this paper, we study these graphs from an algorithmic complexity point of view. We show that wellcovered graph recognition is co-NP-complete and that several other problems are NP-complete for well-covered graphs. A numbe...

A graph G is well-covered if all its maximal independent sets are of the same cardinality. Assume that a weight function w is defined on its vertices. Then G is w-well-covered if all maximal independent sets are of the same weight. For every graph G, the set of weight functions w such that G is w-well-covered is a vector space. Given an input claw-free graph G, we present an O (

‎In this paper we give a characterization of unmixed tripartite‎ ‎graphs under certain conditions which is a generalization of a‎ ‎result of Villarreal on bipartite graphs‎. ‎For bipartite graphs two‎ ‎different characterizations were given by Ravindra and Villarreal‎. ‎We show that these two characterizations imply each other‎.

AIM To compare alcohol purchasing and consumption by ill drinkers in Edinburgh with wider alcohol sales in Scotland. DESIGN Cross-sectional. SETTING Two hospitals in Edinburgh in 2008/09. PARTICIPANTS A total of 377 patients with serious alcohol problems; two-thirds were in-patients with medical, surgical or psychiatric problems due to alcohol; one-third were out-patients. MEASUREMENTS ...