It is proven that if G is a 3-connected claw-free graph which is also Z3-free (where Z3 is a triangle with a path of length 3 attached), P6-free (where P6 is a path with 6 vertices) or H1-free (where H1 consists of two disjoint triangles connected by an edge), then G is hamiltonian-connected. Also, examples will be described that determine a finite family of graphs L such that if a 3-connected ...

Graphs with circular symmetry, called webs, are relevant w.r.t. describing the stable set polytopes of two larger graph classes, quasi-line graphs [9,14] and claw-free graphs [8,9]. Providing a decent linear description of the stable set polytopes of claw-free graphs is a long-standing problem [10]. However, even the problem of finding all facets of stable set polytopes of webs is open. So far,...

Graphs with circular symmetry, called webs, are relevant for describing the stable set polytopes of two larger graph classes, quasi-line graphs [6,10] and claw-free graphs [5,6]. Providing a decent linear description of the stable set polytopes of claw-free graphs is a longstanding problem [7]. However, even the problem of finding all facets of stable set polytopes of webs is open. So far, it i...

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.

The second author’s ω, ∆, χ conjecture proposes that every graph satisties χ ≤ d 1 2 (∆ + 1 + ω)e. In this paper we prove that the conjecture holds for all claw-free graphs. Our approach uses the structure theorem of Chudnovsky and Seymour. Along the way we discuss a stronger local conjecture, and prove that it holds for claw-free graphs with a three-colourable complement. To prove our results ...

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 ...

BACKGROUND Descending control of nociceptive processing, by pathways originating in the rostral ventromedial medulla (RVM) and terminating in the dorsal horn, contributes to behavioural hypersensitivity in a number of pain models. Two facilitatory pathways have been identified and are characterized by serotonin (5-HT) content or expression of the mu opiate receptor. Here we investigated the con...

We studied the relationship between ventricular size and nonspecific periventricular lucency on computed tomograms (leukoaraiosis) in 192 patients with ischemic stroke. Leukoaraiosis did not occur in 21 patients less than 50 years of age; ventricular size could not be measured in an additional 29. Leukoaraiosis was graded from 0 to 4 on a semiquantitative scale; bicaudate, frontal horn, and pos...