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...

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...

Cat’s claw (Uncaria tomentosa) is a medicinal plant from the Amazon River basin that is widely used for inflammatory disorders and was previously described as an inhibitor of NF-kB. Cat’s claw was prepared as a decoction (water extraction) of micropulverized bark with and without concentration by freeze-drying. Murine macrophages (RAW 264.7 cells) were used in cytotoxicity assays (trypan blue e...

Ryjacek [Z. Ryjáček: On a closure concept in claw-free graphs. Journal of Combinatorial Theory Ser. B 70 (1997), 217-224] defined a powerful closure operation cl(G) on claw-free graphs G. Very recently, Ryjacek, Yoshimoto and the talker developed the closure operation cl (G) on claw-free graphs which preserves the (non)-existence of a 2-factor. In this talk, we introduce a closure operation cl(...

A graph G is 1-Hamilton-connected if G − x is Hamilton-connected for every vertex x ∈ V (G). In the paper we introduce a closure concept for 1-Hamiltonconnectedness in claw-free graphs. If G is a (new) closure of a claw-free graph G, then G is 1-Hamilton-connected if and only if G is 1-Hamilton-connected, G is the line graph of a multigraph, and for some x ∈ V (G), G − x is the line graph of a ...

We prove that claw-free graphs, containing an induced dominating path, have a Hamiltonian path, and that 2-connected claw-free graphs, containing an induced doubly dominating cycle or a pair of vertices such that there exist two internally disjoint induced dominating paths connecting them, have a Hamiltonian cycle. As a consequence, we obtain linear time algorithms for both problems if the inpu...