Finding augmenting chains is in the heart of the maximum matching problem, which is equivalent to the maximum stable set problem in the class of line graphs. Due to the celebrated result of Edmonds, augmenting chains can be found in line graphs in polynomial time. Minty and Sbihi generalized this result to claw-free graphs. In this paper we extend it to larger classes. As a particular consequen...

We determine the maximum number of edges that a claw-free graph can have, when its maximum degree and matching number are bounded. This is a famous problem that has been studied on general graphs, and for which there is a tight bound. The graphs achieving this bound contain in most cases an induced copy of K1,3, the claw, which motivates studying the question on claw-free graphs. Note that on g...

This paper presents a multimedia intelligent tutoring system that teaches context-free grammar. The tutor model of this ITS is composed of a set of teaching strategies and an algorithm that determines which teaching action to be deployed given the goals of the system and the current state of the student model. The student model uses the Constraint-Based Modeling (CBM) approach in diagnosing the...

A set M of edges of a graph G is a matching if no two edges in M are incident to the same vertex. A set S of vertices in G is a total dominating set ofG if every vertex of G is adjacent to some vertex in S. The matching number is the maximum cardinality of a matching of G, while the total domination number of G is the minimum cardinality of a total dominating set of G. In this paper, we investi...

The augmenting chain technique has been applied to solve the maximum stable set problem in the class of line graphs (which coincides with the maximum matching problem) and then has been extended to the class of claw-free graphs. In the present paper, we propose a further generalization of this approach. Specifically, we show how to find an augmenting chain in graphs containing no skew star, i.e...

In this work, we investigate in the problem of perfect matchings with prescribed matchings in the n-dimensional hypercube network Qn. We obtain the following contributions: For any arbitrary matching with at most n − 1 edges, it can be extended to a perfect matching of Qn for n ≥ 1. Furthermore, for any arbitrary non-forbidden matching with n edges, it also can be extended to a perfect matching...

We complete a classification of the groups of endotrivial modules for the modular group algebras of symmetric groups and alternating groups. We show that, for n p2, the torsion subgroup of the group of endotrivial modules for the symmetric groups is generated by the sign representation. The torsion subgroup is trivial for the alternating groups. The torsion-free part of the group is free abelia...

we present a matching and lp based heuristic algorithm that decides graph non-hamiltonicity. each of the n! hamilton cycles in a complete directed graph on n + 1 vertices corresponds with each of the n! n-permutation matrices p, such that pu,i = 1 if and only if the ith arc in a cycle enters vertex u, starting and ending at vertex n + 1. a graph instance (g) is initially coded as exclusion set ...