arc transitive

Highly arc transitive two ended digraphs ★★

Conjecture If $G$ is a highly arc transitive digraph with two ends, then every tile of $G$ is a disjoint union of complete bipartite graphs.

Keywords: arc transitive; digraph; infinite graph

Posted by mdevos
updated October 29th, 2007

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Graph Theory » Infinite Graphs

Universal highly arc transitive digraphs ★★★

Author(s): Cameron; Praeger; Wormald

An alternating walk in a digraph is a walk $v_0,e_1,v_1,\ldots,v_m$ so that the vertex $v_i$ is either the head of both $e_i$ and $e_{i+1}$ or the tail of both $e_i$ and $e_{i+1}$ for every $1 \le i \le m-1$ . A digraph is universal if for every pair of edges $e,f$ , there is an alternating walk containing both $e$ and $f$