It is shown that every 3-connected claw-free graph having at most 6 − 7 vertices is hamiltonian, where is the minimum degree. c © 2002 Elsevier Science B.V. All rights reserved.

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 ...

abstract: regular consumption of seafood has been widely recommended by the authorities. however, some species especially benthic crustaceans accumulate heavy metals. in addition, the health risks associated to the consumption of such seafood might increase if the consumers use cooking methods that enhance the concentration of heavy metals. in this study, the effects of different cooking method...

The Caribbean spiny lobster, Panulirus argus, is distributed from Brazil throughout the Caribbean and the Gulf of Mexico to approximately North Carolina and Bermuda (Holthius, 1991). It supports major commercial fi sheries in Florida, the Caribbean and Brazil. Commercially, P. argus is especially important to the state of Florida, where the spiny lobster fi shery ranks second only to shrimp in ...