l-Regular rotations of the countably infinite complete graph

P Finite Automata and Regular Languages over Countably Infinite Alphabets

We examine the class of languages over countably infinite alphabets characterized by a class of restricted and simplified P automata variants, which we call P finite automata, and show that these classes possess several properties which make them perfect candidates for being the natural extension of the notion of finite automata and that of regular languages to infinite alphabets. To this aim, ...

Distance regular covers of the complete graph

Distance regular graphs fall into three families: primitive, antipodal, and bipar-tite. Each antipodal distance regular graph is a covering graph of a smaller (usually primitive) distance regular graph; the antipodal distance graphs of diameter three are covers of the complete graph, and are the first non-trivial case. Many of the known examples are connected with geometric objects, such as pro...

The regular spaces with countably based models

Ramsey Properties of Countably Infinite Partial Orderings

A partial ordering P is chain-Ramsey if, for every natural number n and every coloring of the n-element chains from P in finitely many colors, there is a monochromatic subordering Q isomorphic to P. Chain-Ramsey partial orderings stratify naturally into levels. We show that a countably infinite partial ordering with finite levels is chain-Ramsey if and only if it is biembeddable with one of a c...

Arc-transitive regular cyclic covers of the complete bipartite graph

Characterizing regular covers of edge-transitive or arc-transitive graphs is currently a hot topic in algebraic graph theory. In this paper, we will classify arctransitive regular cyclic covers of the complete bipartite graph Kp,p for each odd prime p. The classification consists of four infinite families of graphs. In particular, such covers exist for each odd prime p. The regular elementary a...