Let G be a graph on n t> 3 vertices. Dirac's minimum degree condition is the condition that all vertices of G have degree at least in. This is a well-known sufficient condition for the existence of a Hamilton cycle in G. We give related sufficiency conditions for the existence of a Hamilton cycle or a perfect matching involving a restriction of Dirac's minimum degree condition to certain subset...

Let δ(G) denote the minimum degree of a graph G. We prove that for t ≥ 4 and k ≥ 2, a graph G of order at least (t + 1)k + 11 6 t 2 with δ(G) ≥ k + t − 1 contains k pairwise vertex-disjoint copies of K1,t.

Dromaeosaurid theropod dinosaurs possess a strongly recurved, hypertrophied and hyperextensible ungual claw on pedal digit II. This feature is usually suggested to have functioned as a device for disembowelling herbivorous dinosaurs during predation. However, modelling of dromaeosaurid hindlimb function using a robotic model and comparison of pedal ungual morphology with extant analogue taxa bo...

We prove that the genus polynomials of the graphs called iterated claws are real-rooted. This continues our work directed toward the 25-year-old conjecture that the genus distribution of every graph is log-concave. We have previously established log-concavity for sequences of graphs constructed by iterative vertexamalgamation or iterative edge-amalgamation of graphs that satisfy a commonly obse...

The poorly understood Triassic reptile Drepanosaurus is known for its excessively large claws. New discoveries demonstrate a remarkable modification of the bones in the wrist and forearm, a significant departure from the typical five-digit tetrapod limb.

The digital cushion is an essential part of maintaining a healthy foot, working to dissipate foot strike and body weight forces lameness from claw horn disruption lesions. Despite the importance cushion, little known about basic anatomy, adipocyte morphology, fatty acid composition in relation age, limb position, condition score. In total, 60 claws (from 17 cows) were selected collected herd, e...