Pathological claw formations occur subsequent to irregular or prolonged claw trimming periods and as a result of improper flooring. Clinical experience and material testing finds horn of minor quality to be associated with the malformations. Finite element models (FEM) of a flat claw (FC), a contracted claw (CC), and a laminitic claw (LC) were designed from native claw specimens to combine mate...

We propose a new type of claw free function family, a pseudo self-de nable claw free function family , which provides, by Damg ard's construction, a collision intractable hash function family that is more suitable in several cryptographic applications such as digital signature, bit commitment, etc. We give an example of self-de nable claw free function families based on the hardness of some num...

A graph is claw-free if no vertex has three pairwise nonadjacent neighbours. At first sight, there seem to be a great variety of types of claw-free graphs. For instance, there are line graphs, the graph of the icosahedron, complements of triangle-free graphs, and the Schläfli graph (an amazingly highly-symmetric graph with 27 vertices), and more; for instance, if we arrange vertices in a circle...

An 8-year-old male Golden Retriever had lameness and claw abnormality in the second digit of the left forelimb. Radiography revealed osteomyelitis in the distal phalanx bone of the affected limb. Microscopic examination of the claw revealed numerous hyphae in the claw matrix. Fungal DNA fragments coding the ribosomal internal transcribed spacer region (ITS) were detected from the claw matrix as...

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...

Providing a complete description of the stable set polytopes of claw-free graphs is a longstanding open problem since almost twenty years. Eisenbrandt et al. recently achieved a breakthrough for the subclass of quasi-line graphs. As a consequence, every non-trivial facet of their stable set polytope is of the form k ∑ v∈V1 xv+(k+1) ∑ v∈V2 xv ≤ b for some positive integers k and b, and non-empty...

We present a new graph composition that produces a graph G from a given graph H and a fixed graph B called gear and we study its polyhedral properties. This composition yields counterexamples to a conjecture on the facial structure of STAB(G) when G is claw-free.

A graph is claw-free if no vertex has three pairwise nonadjacent neighbours. In this series of papers we give a structural description of all claw-free graphs. In this paper, we achieve a major part of that goal; we prove that every claw-free graph either belongs to one of a few basic classes, or admits a decomposition in a useful way.

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...