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arXiv · 1110.2945

Highly arc-transitive digraphs -- counterexamples and structure

Matt DeVos·Bojan Mohar·Robert Šámal
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Abstract

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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Matt DeVos, Bojan Mohar, Robert Šámal. 2013-10-10. Highly arc-transitive digraphs -- counterexamples and structure. https://arxiv.org/abs/1110.2945

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