Highly arc-transitive digraphs - Structure and counterexamples
نویسندگان
چکیده
Two problems of Cameron, Praeger, and Wormald [Infinite highly arc transitive digraphs and universal covering digraphs, Combinatorica (1993)] are resolved. First, locally finite highly arc-transitive digraphs with universal reachability relation are presented. Second, constructions of two-ended highly arc-transitive digraphs are provided, where each ‘building block’ is a finite bipartite digraph that is not a disjoint union of complete bipartite digraphs. Both of these were conjectured impossible in the above-mentioned paper. We also describe the structure of two-ended highly arc-transitive digraphs in more generality, heading towards a characterization of such digraphs. However, the complete characterization
منابع مشابه
Highly arc-transitive digraphs – counterexamples and structure∗
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...
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ورودعنوان ژورنال:
- Combinatorica
دوره 35 شماره
صفحات -
تاریخ انتشار 2015