# arc transitive

## Highly arc transitive two ended digraphs ★★

Author(s): Cameron; Praeger; Wormald

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

Keywords: arc transitive; digraph; infinite graph

## Universal highly arc transitive digraphs ★★★

Author(s): Cameron; Praeger; Wormald

An *alternating* walk in a digraph is a walk so that the vertex is either the head of both and or the tail of both and for every . A digraph is *universal* if for every pair of edges , there is an alternating walk containing both and

**Question**Does there exist a locally finite highly arc transitive digraph which is universal?

Keywords: arc transitive; digraph