Yannakakis’ Clique versus Independent Set problem (CL− IS) in communication complexity asks for the minimum number of cuts separating cliques from stable sets in a graph, called CS-separator. Yannakakis provides a quasi-polynomial CS-separator, i.e. of size O(n), and addresses the problem of finding a polynomial CS-separator. This question is still open even for perfect graphs. We show that a p...

A cycle C in a graph G is said to be dominating if E(G−C) = ∅. Enomoto et al. showed that if G is a 2-connected triangle-free graph with α(G) ≤ 2κ(G) − 2, then every longest cycle is dominating. But it is unknown whether the condition on the independence number is sharp. In this paper, we show that if G is a 2-connected triangle-free graph with α(G) ≤ 2κ(G) − 1, then G has a longest cycle which...

A graphG is fractional ID-[a, b]-factor-critical ifG−I includes a fractional [a, b]-factor for every independent set I of G. In this paper, it is proved that if α(G) ≤ 4b(δ(G)−a+1) (a+1)2+4b , then G is fractional ID-[a, b]-factor-critical. Furthermore, it is shown that the result is best possible in some sense.

The Maximum Independent Set problem often arises in the following form: given n tasks which compete for the same resources, compute the largest set of tasks which can be performed at the same time without sharing resources. More generally, in case the tasks have weights (priorities), one may ask for the set of tasks of largest total weight which can be performed at the same time. This is called...

Let n(G) and α(G) be the order and the independence number of a graph G, repsectively. If G is bipartite graph, then it is well-known and easy to see that α(G) ≥ n(G) 2 . In this paper we present a constructive characterization of bipartite graphs G for which

In this paper cores and stable sets for games with fuzzy coalitions are introduced and their relations studied. For convex fuzzy games it turns out that all cores coincide and that the core is the unique stable set. Also relations between cores and stable sets for fuzzy clan games are discussed. MSC: 90D12; 03E72

The MIS data is critical to an organization and should be protected from misuse by wrong persons. Although The MIS data is typically meant for the senior managers each MIS report may not be required by every manager. The access to MIS data is determined by the role of an individual in the organization and controlled by the MIS administrator accordingly. The access is generally determined by the...

We prove that there is an absolute constant C > 0 so that for every natural n there exists a trianglefree regular graph with no independent set of size at least C √ n log n.

The question of the relevance of MIS research to practitioners is part of the broader question of the match between academic research goals and the goals of constituents. We call for a broader conception of who those constituents might be, and the implications that has for the activities of MIS academics.

We show that a graph with minimum degree δ, independence number α ≥ δ and without isolated vertices, possesses a partition by vertex-disjoint cycles and atmost α−δ+1 edges or vertices. © 2008 Elsevier B.V. All rights reserved.