An n-by-n bipartite graph is H-saturated if the addition of any missing edge between its two parts creates a new copy of H. In 1964, Erdős, Hajnal and Moon made a conjecture on the minimum number of edges in a Ks,s-saturated bipartite graph. This conjecture was proved independently by Wessel and Bollobás in a more general, but ordered, setting: they showed that the minimum number of edges in a ...

In this paper, we introduce a new class algebras related to BCK-algebras and semigroups, called a KS-semigroup and define an ideal of a KS-semigroups and a strong KS-semigroup, and characterizations of ideals is given. Also we define a congruence relation on a KS-semigroups and a quotient KS-semigroups and prove the isomorphism. Mathematics Subject Classification: 06F35, 03G25

background: the most common chromosomal abnormality due to non-obstructive azoospermia (noa) is klinefelter syndrome (ks) which occurs in 1-1.72 out of 500-1000 male infants. the probability of retrieving sperm as the outcome could be asymmetrically different between patients with and without ks, therefore logistic regression analysis is not a well-qualified test for this type of data. this stu...

background kaposi sarcoma (ks) is an angioproliferative tumor that mainly involves mucocutaneous tissues, but extracutaneous spread to lymph nodes, gi tract, lungs, liver, pancreas, heart, and testes can occur in aids-associated ks. patients with pulmonary ks may be symptomatic or present with an asymptomatic abnormality on chest radiography. patient and method a 28-year-old man presented with ...

Kabuki syndrome (KS) is a rare genetic disease with a distinctive dysmorphic face, intellectual disability, and multiple congenital abnormalities. KS is inherited in an autosomal dominant manner. As the primary cause of KS, MLL2 mutations have been identified in 56-76% of affected individuals who have been tested, suggesting that there may be additional genes associated with KS. Recently, a few...