We introduce a new class of graphs which we call P3-dominated graphs. This class properly contains all quasi-claw-free graphs, and hence all claw-free graphs. Let G be a 2-connected P3-dominated graph. We prove that G is hamiltonian if α(G) ≤ κ(G), with two exceptions: K2,3 and K1,1,3. We also prove that G is hamiltonian if G is 3-connected and |V (G)| ≤ 5δ(G) − 5. These results extend known re...

A dairy cow’s environment may influence the onset of laminitis and associated claw horn lesions by exacerbating changes in the hoof triggered by events at parturition, onset of subacute ruminal acidosis, or claw horn growth and wear and ground reaction forces on different walking surfaces. Environmental risk factors for laminitis and associated claw horn lesions include feed bunk space and desi...

Dromaeosaurid theropod dinosaurs, such as Velociraptor, possess strongly recurved, hypertrophied and hyperextensible ungual claws on the pes (digit II) and manus. The morphology of these unguals has been linked to the capture and despatching of prey. However, the mechanical properties or, more importantly, the mechanical potential of these structures have not been explored. Generation of a 3D f...

We show that if G is a 4-connected claw-free graph in which every induced hourglass subgraph S contains two non-adjacent vertices with a common neighbor outside S, then G is hamiltonian. This extends the fact that 4-connected claw-free, hourglass-free graphs are hamiltonian, thus proving a broader special case of a conjecture by Matthews and Sumner.

Cave animals are often adapted to digging and life underground, with claw toes similar in structure and function to a sampling scoop. In this paper, the clawed toes of the Himalayan marmot were selected as a biological prototype for bionic research. Based on geometric parameter optimization of the clawed toes, a bionic sampling scoop for use on Mars was designed. Using a 3D laser scanner, the p...

We study methods of planarizing and acyclically coloring claw-free subcubic graphs. We give a polynomial-time algorithm that, given such a graph G, produces an independent set Q of at most n/6 vertices whose removal from G leaves an induced planar subgraph P (in fact, P has treewidth at most four). We further show the stronger result that in polynomial-time a set of at most n/6 edges can be ide...