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