Graphs with circular symmetry, called webs, are relevant w.r.t. describing the stable set polytopes of two larger graph classes, quasi-line graphs [8,12] and claw-free graphs [7,8]. Providing a decent linear description of the stable set polytopes of claw-free graphs is a long-standing problem [9]. Ben Rebea conjectured a description for quasi-line graphs, see [12]; Chudnovsky and Seymour [2] v...

We show that deciding whether a given graph G of size m has a unique perfect matching as well as finding that matching, if it exists, can be done in time O(m) if G is either a cograph, or a split graph, or an interval graph, or claw-free. Furthermore, we provide a constructive characterization of the claw-free graphs with a unique perfect matching.

If G is a claw-free graph of sufficiently large order n, satisfying a degree condition σk > n+k2−4k+7 (where k is an arbitrary constant), then G has a 2-factor with at most k − 1 components. As a second main result, we present classes of graphs C1, . . . , C8 such that every sufficiently large connected claw-free graph satisfying degree condition σ6(k) > n + 19 (or, as a corollary, δ(G) > n+19 ...

In this article, we prove that a line graph with minimum degree δ ≥ 7 has a spanning subgraph in which every component is a clique of order at least three. This implies that if G is a line graph with δ ≥ 7, then for any independent set S there is a 2-factor of G such that each cycle contains at most one vertex of S. This supports the conjecture that δ ≥ 5 is sufficient to imply the existence of...

In this paper, we present several conditions for K1;3-free graphs, which guarantee the graph is subpancyclic. In particular, we show that every K1;3-free graph with a minimum degree sum 2 ¿ 2 √ 3n+ 1 − 4; every {K1;3; P7}-free graph with 2 ¿ 9; every {K1;3; Z4}-free graph with 2 ¿ 9; and every K1;3-free graph with maximum degree , diam(G)¡ ( +6)=4 and 2 ¿ 9 is subpancyclic. c © 2002 Elsevier Sc...

Thomassen conjectured that every 4-connected line graph is hamiltonian. It has been proved that every 4-connected line graph of a claw-free graph, or an almost claw-free graph, or a quasi-claw-free graph, is hamiltonian. In 1998, Ainouche et al. [2] introduced the class of DCT graphs, which properly contains both the almost claw-free graphs and the quasi-claw-free graphs. Recently, Broersma and...