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...

A graph is equimatchable if all of its maximal matchings have the same size. A graph is claw-free if it does not have a claw as an induced subgraph. In this paper, we provide, to the best of our knowledge, the first characterization of claw-free equimatchable graphs by identifying the equimatchable clawfree graph families. This characterization implies an efficient recognition algorithm.

In Stanley’s seminal 1995 paper on the chromatic symmetric function, he stated that there was no known graph that was not contractible to the claw and whose chromatic symmetric function was not e-positive, namely, not a positive linear combination of elementary symmetric functions. We resolve this by giving infinite families of graphs that are not contractible to the claw and whose chromatic sy...

this study was performed to determine the effect of copper on growth performance, blood metabolites and claw health in young holstein bulls in a humid area in north of iran. one hundred and two young holstein bulls (initial body weight= 377.3±17.1 kg) were randomly allocated to two treatments in a completely randomized design for 56 days. the treatment groups received: (1) the basal diet of no ...

1. Previous evidence demonstrates that closing force decreases proportionally as fiddler crab claw size increases. Larger crabs do have greater absolute closing force, but less than would be expected if claw proportions were isometric. In the Mud Fiddler Crab, Uca pugnax , this is explained by a decrease in mechanical advantage with increasing claw size. 2. We here re-measure mechanical advanta...

In this paper, we prove that a 2-connected weighted graph G contains either a Hamilton cycle or a cycle of weight at least 2m/3 if it satisfies the following conditions: (1) ∑3 i=1 d (vi) ≥ m, where v1, v2 and v3 are three pairwise nonadjacent vertices of G, and two of them are nonadjacent vertices of an induced claw or an induced modified claw; (2) In each induced claw and each induced modifie...

claw capsule lesions are the most common cause’s lameness in cows. during the entire year of 2005 a survey was undertaken by sir author on the prevalence of different claw lesions causing lameness on 30882 cases of culled cows and bulls at central abttoir in the vicinity of ardebil which was well equiped and with new constructions. after recording information for each case, the feet were amputa...

A stable cutset in a connected graph is a stable set whose deletion disconnects the graph. Let K4 and K1,3 (claw) denote the complete (bipartite) graph on 4 and 1+ 3 vertices. It is NP-complete to decide whether a line graph (hence a claw-free graph) with maximum degree five or a K4-free graph admits a stable cutset. Here we describe algorithms deciding in polynomial time whether a claw-free gr...