Factor-criticality and matching extension in DCT-graphs

The class of DCT-graphs is a common generalization of the classes of almost claw-free and quasi claw-free graphs. We prove that every even (2p + 1)-connected DCT-graph G is p-extendable, i.e. every set of p independent edges of G is contained in a perfect matching of G. This result is obtained as a corollary of a stronger result concerning factor-criticality of DCT-graphs

Forbidden Subgraphs, Hamiltonicity and Closure in Claw-Free Graphs

We study the stability of some classes of graphs defined in terms of forbidden subgraphs under the closure operation introduced by the second author. Using these results, we prove that every 2-connected claw-free and P 7 -free, or claw-free and Z 4 - free, or claw-free and eiffel-free graph is either hamiltonian or belongs to a certain class of exceptions (all of them having connectivity 2). 1 Introduction In this paper we consider only finite undirected graphs G = (V (G); E(G)) without loops and multiple edges. For terminology and notation not defined here we refer to [3]. If H 1 ; : : : ; H k (k 1) are graphs, then we say that a graph G is H 1 : : : H k -free if G contains no copy of any of the graphs H 1 ; : : : ; H k as an induced subgraph; the graphs H 1 ; : : : ; H k will be also referred to in this context as forbidden subgraphs. Specifically, the four-vertex star K 1;3 will be also denoted by C and called the claw and in this case we say that G is claw-free. Whenever we..