Let it(G) be the number of independent sets of size t in a graph G. Engbers and Galvin asked how large it(G) could be in graphs with minimum degree at least δ. They further conjectured that when n ≥ 2δ and t ≥ 3, it(G) is maximized by the complete bipartite graph Kδ,n−δ. This conjecture has drawn the attention of many researchers recently. In this short note, we prove this conjecture.

We study separable metric spaces with few types of countable dense sets. We present a structure theorem for locally compact spaces having precisely n types of countable dense sets: such a space contains a subset S of size at most n−1 such that S is invariant under all homeomorphisms of X and X \ S is countable dense homogeneous. We prove that every Borel space having fewer than c types of count...

In Berend and Kontorovich (2012), the following problem was studied: A random sample of size t is taken from a world (i.e., probability space) of size n; bound the expected value of the probability of the set of elements not appearing in the sample (unseen mass) in terms of t and n. Here we study the same problem, where the world may be countably infinite, and the probability measure on it is r...

A collection of Il 3-cube decompositions of a graph G is said to have intersection size t if there is a set S, with 181 = t, of 3-cubes which is contained in every decomposition, and no 3-cube which is not in S occurs in more than one decomposition. We determine all integers n, t and Il, with Il ::; 12, for which there exists a collection of Il 3-cube decompositions of Kn with intersection size...

introduction: studies on behavioral patterns and personality traits play a critical role in the prediction of healthy or unhealthy behaviors and identification of high-risk individuals for cardiovascular diseases (cvds) in order to implement preventive strategies. this study aimed to compare personality types in individuals with and without cvd based on the enneagram of personality. materials a...

Type parameterization is the ability to defrne a type in terms of another, unspecifled, type. Versions of the parameterized type may then be created for several particular parameter types. A language supporting type parameterization allows specification ofgeneral container types such as list, vector, and associative array where the specific type of the elements is left as a parameter. Thus, a p...

Background Neurofibromatosis is an autosomal dominant disease. It affects one in 2,700 to 3,300 people. The main gene mutated in the disease is a tumor suppressor protein called neurofibromin. There are several categories, the most important of which is divided into two types of type I and type 2 neurofibromatosis. Here, we aimed to identify th...

Spectral reflectance patterns of corals are driven largely by the pigments of photosynthetic symbionts within the host cnidarian. The warm inshore bays and cooler offshore reefs of Palau share a variety of coral species with differing endosymbiotic dinoflagellates (genus: Symbiodinium), with the thermally tolerant Symbiodinium trenchii (S. trenchii) (= type D1a or D1-4) predominating under the ...

Usually dimension should be an integer valued parameter. We introduce a refined version of dimension for graphs, which can assume a value 1⁄2 t 1l t , thought to be between t 1 and t. We have the following two results: (a) a graph is outerplanar if and only if its dimension is at most 1⁄22l3 . This characterization of outerplanar graphs is closely related to the celebrated result of W. Schnyder...

case 0: /* just waste a cycle and loop */ break; case 1: /* use the first output from two cycles */ *buf++ ^= nltap(R, r) ^ 0x69; r = cycle(R, r); break; case 2: /* use the second output from two cycles */ r = cycle(R, r); *buf++ ^= nltap(R, r); break; case 3: /* return from one cycle */ *buf++ ^= nltap(R, r) ^ 0x96; break; } } } /* encrypt/decrypt a frame of data */ void sober_genbytes(unsigne...