Objective(s): Asthma, the most frequent chronic respiratory disease, results from a complex interaction between multiple genes and environmental factors. To date, more than 100 candidate genes and single nucleotide polymorphisms (SNPs) have been reported to be associated with asthma. One of the discovered genes related to asthma is ADAM33. However, the relationship between ADAM33 gene polymorph...

The paper shows that there is no finite set of forbidden minors which characterizes classes of independence models that are representable by Gaussian, discrete and binary distributions, respectively. In addition, a way to prove the nonexistence of a finite characterization for any other class of independence models is suggested. MSC 2000: 60A99, 68T30, 94A15

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In this paper, we obtain a forbidden-minor characterization of the class of binary gammoids M such that, for every pair of elements x, y of M, both the splitting matroid Mx,y and the element splitting matroid M ′ x,y are binary gammoids.

A connected edge-colored graphG is said to be rainbow-connected if any two distinct vertices of G are connected by a path whose edges have pairwise distinct colors, and the rainbow connection number rc(G) ofG is the minimum number of colors that can make G rainbow-connected. We consider families F of connected graphs for which there is a constant kF such that every connected F-free graph G with...

Categorical skew lattices are a variety of skew lattices on which the natural partial order is especially well behaved. While most skew lattices of interest are categorical, not all are. They are characterized by a countable family of forbidden subalgebras. We also consider the subclass of strictly categorical skew lattices.

We characterize graphs that have intersection representations using unit intervals with open or closed ends such that all ends of the intervals are integral in terms of infinitely many minimal forbidden induced subgraphs. Furthermore, we provide a quadratic-time algorithm that decides if a given interval graph admits such an intersection representation.