Providing a complete description of the stable set polytopes of claw-free graphs is a longstanding open problem since almost twenty years. Eisenbrandt et al. recently achieved a breakthrough for the subclass of quasi-line graphs. As a consequence, every non-trivial facet of their stable set polytope is of the form k ∑ v∈V1 xv+(k+1) ∑ v∈V2 xv ≤ b for some positive integers k and b, and non-empty...

We present a new graph composition that produces a graph G from a given graph H and a fixed graph B called gear and we study its polyhedral properties. This composition yields counterexamples to a conjecture on the facial structure of STAB(G) when G is claw-free.

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.

Juvenile cystic adenomyoma is a rare form of adenomyosis and described as a new type of mullerian anomaly in literature. We are presenting two cases of juvenile cystic adenomyoma which were misdiagnosed preoperatively as unicornuate uterus with haematometra in a non-communicating rudimentary horn. The mainstay of treatment is complete resection of lesion.

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.

background: microcystic adnexal tumor is a rare sclerosing variant of ductal carcinoma of eccrine sweat glands which is highly invasive. this tumor is often misdiagnosed as other benign or malignant skin lesions and improper treatment is carried on and is associated with high recurrence rate. case presentation: we reported here in a 59-years old man who underwent incisional biopsy for a ongenit...

Giant cutaneous horns (GCH) present as isolated skin lesions with large corneous components of considerable morphologic variation. Despite their striking clinical appearance, prevalence statistics are unknown due to their rarity. Diagnosis of the underlying pathology is essential for appropriate management, as a significant proportion of cutaneous horns arise in the setting of a cutaneous malig...

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...