A graph on n vertices which is the union of two comparability graphs on the same vertex set, always contains a clique or independent set of size n 1 3 . On the other hand, there exist such graphs for which the largest clique and independent set are of size at most n. Similar results are obtained for graphs which are a union of a fixed number k of comparability graphs. We also show that the same...

For a graph G = (V,E), a set S ⊆ V is a restrained dominating set if every vertex not in S is adjacent to a vertex in S as well as another vertex in V − S. The restrained domination number of G, denoted by γr(G), is the smallest cardinality of a restrained dominating set of G. In this paper we find all graphs G satisfying γr(G) = n− 3, where n is the order of G.

A set S of vertices of a graph G is a total dominating set if every vertex of V (G) is adjacent to some vertex in S. We provide three equivalent conditions for a tree to have a unique minimum total dominating set and give a constructive characterization of such trees.

A set S of vertices of a graph G is a total dominating set if every vertex of V (G) is adjacent to some vertex in S. The total domination number t(G) is the minimum cardinality of a total dominating set of G. Let G be a connected spanning subgraph of Ks;s, and let H be the complement of G relative to Ks;s; that is, Ks;s = G ⊕ H is a factorization of Ks;s. The graph G is k-supercritical relative...

Let F be a family of translates of a fixed convex set M in Rn. Let (F) and (F) denote the transversal number and the independence number of F, respectively. We show that (F) (F) 8 (F) − 5 for n = 2 and (F) 2n−1nn (F) for n 3. Furthermore, if M is centrally symmetric convex body in the plane, then (F) (F) 6 (F)− 3. © 2006 Elsevier B.V. All rights reserved.

We partition the fast escaping set of a transcendental entire function into two subsets, the maximally fast escaping set and the non-maximally fast escaping set. These sets are shown to have strong dynamical properties. We show that the intersection of the Julia set with the non-maximally fast escaping set is never empty. The proof uses a new covering result for annuli, which is of wider intere...

Planning for a successful MIS implementation requires understanding the effects of the introduction of a new system on the work lives of potential adopters. The effects can be assessed by the MIS practitioner/ change agent ff the agent will first obtain a thorough and specific understanding of the task activities performed by potential adopters, the interactions they engage in as they perform t...

This note investigates the noncooperative foundations of von Neumann-Morgenstern (vN-M) stable sets in voting games. To do so, we study subgame perfect equilibria of a noncooperative legislative bargaining game, based on underlying simple games. The following results emerge from such an exercise: Every stable set of the underlying simple game is the limit set of undominated pure-strategy Markov...

Experiential learning activities (ELAs) that are industry-partnered and real-world problem-based can provide undergraduate students with concrete experiences of using information technologies in the field. Flow theory provides a theoretical basis to guide the design of ELAs, ensuring that the goals are clear, feedback is explicit, and the challenges and skills are balanced. Based on this theory...

We determine the maximal cocliques of size ≥ 4q2 + 5q + 5 in the Kneser graph on point-plane flags in PG(4, q). The maximal size of a coclique in this graph is (q2 + q + 1)(q3 + q2 + q + 1).