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.

Operant conditioning is a common tool for studying cognitive aspects of brain functions. As the first step toward understanding those functions in simple invertebrate microbrains, we tested whether operant conditioning could be applied to train American lobster Homarus americanus that has been extensively adopted as an animal model for neurophysiological analyses of nervous system functions and...

1. A protein component, fraction B, of lobster nerve extracts has been isolated and purified by differential ultracentrifugation and precipitation with zinc acetate. 2. Physicochemical data obtained from this protein and from fraction C are summarized. 3. Fraction B is present in lobster nerve extracts in higher concentration (relative to fraction A) than in blood. 4. A second component, fracti...

The insulin signalling system is one of the most conserved endocrine systems of Animalia from mollusc to man. In decapod Crustacea, such as the Eastern spiny lobster, Sagmariasus verreauxi (Sv) and the red-claw crayfish, Cherax quadricarinatus (Cq), insulin endocrinology governs male sexual differentiation through the action of a male-specific, insulin-like androgenic gland peptide (IAG). To un...

Organisms in natural habitats must frequently respond to changes in their environments through various physiological mechanisms. My laboratory has developed several methods for the quantification of stress in crustaceans. An ELISA was developed for the crustacean hyperglycemic hormone (CHH) from the American lobster (Homarus americanus). It is sensitive to as little as 0.2 fmol of peptide. Incr...

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.

Fishing can trigger trophic cascades that alter community structure and dynamics and thus modify ecosystem attributes. We combined ecological data of sea urchin and macroalgal abundance with fishery data of spiny lobster (Panulirus interruptus) landings to evaluate whether: (1) patterns in the abundance and biomass among lobster (predator), sea urchins (grazer), and macroalgae (primary producer...

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...