Highly arc-transitive digraphs -- counterexamples and structure

Details Highly arc-transitive digraphs -- counterexamples and structure Highly arc-transitive digraphs -- counterexamples and structure

2011-10-13

arxiv.org/abs/1110.2945v1

Mathematics

Combinatorics

Scientific paper

We resolve two problems of [Cameron, Praeger, and Wormald -- Infinite highly arc transitive digraphs and universal covering digraphs, Combinatorica 1993]. First, we construct a locally finite highly arc-transitive digraph with universal reachability relation. Second, we provide constructions of 2-ended highly arc transitive digraphs where each `building block' is a finite bipartite graph that is not a disjoint union of complete bipartite graphs. This was conjectured impossible in the above paper. We also describe the structure of 2-ended highly arc transitive digraphs in more generality, although complete characterization remains elusive.

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