© 2018 Elsevier Inc. We apply the theory of Bruhat–Tits trees to the study of optimal embeddings from orders of rank two and three to quaternion algebras. Specifically, we determine how many conjugacy classes of global ...

We propose the following conjecture: For every fixed alpha is an element of [0, 1/3), each graph of minimum degree at least (1 + alpha)k/2 and maximum degree at least 2(1 - alpha)k contains each tree with k edges as a ...

We apply the theory of Bruhat-Tits trees to the study of optimal embeddings from orders of rank two and three to quaternion algebras. Specifically, we determine how many conjugacy classes of global Eichler orders in an ...

This is the last of a series of four papers in which we prove the following relaxation of the Loebl-Komlós-Sós conjecture: For every α > 0 there exists a number k0 such that for every k > k0, every n-vertex graph G ...

Let k be a local field and let be the two-by-two matrix algebra over k. In our previous work, we developed a theory that allows the computation of the set of maximal orders in containing a given suborder. This set is given ...

An (n, d)-expander is a graph G = (V, E) such that for every X subset of V with vertical bar X vertical bar <= 2n - 2 we have vertical bar Gamma(G)(X) vertical bar >= (d + 1) vertical bar X vertical bar. A tree T is small ...