Cameron, Peter J.

Cores of strongly regular graphs ★★★

Author(s): Cameron; Kazanidis

Question   Does every strongly regular graph have either itself or a complete graph as a core?

Keywords: core; strongly regular

Highly arc transitive two ended digraphs ★★

Author(s): Cameron; Praeger; Wormald

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

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 $

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

Keywords: arc transitive; digraph

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