Edge-colourings of cubic graphs admitting a solvable vertex-transitive group of automorphisms

Edge-colourings of cubic graphs admitting a solvable vertex-transitive group of automorphisms

On Cubic Graphs Admitting an Edge-Transitive Solvable Group

Using covering graph techniques, a structural result about connected cubic simple graphs admitting an edge-transitive solvable group of automorphisms is proved. This implies, among other, that every such graph can be obtained from either the 3-dipole Dip3 or the complete graph K4, by a sequence of elementary-abelian covers. Another consequence of the main structural result is that the action of...

Semiregular Automorphisms of Cubic Vertex Transitive Graphs

It is shown that for a connected cubic graph Γ , a vertex transitive group G ≤ AutΓ contains a large semiregular subgroup. This confirms a conjecture of Cameron and Sheehan (2001).

Semiregular Automorphisms of Cubic Vertex-transitive Graphs

We characterise connected cubic graphs admitting a vertextransitive group of automorphisms with an abelian normal subgroup that is not semiregular. We illustrate the utility of this result by using it to prove that the order of a semiregular subgroup of maximum order in a vertex-transitive group of automorphisms of a connected cubic graph grows with the order of the graph, settling [2, Problem ...

Semiregular automorphisms of vertex-transitive cubic graphs

An old conjecture of Marušič, Jordan and Klin asserts that any finite vertextransitive graph has a non-trivial semiregular automorphism. Marušič and Scapellato proved this for cubic graphs. For these graphs, we make a stronger conjecture, to the effect that there is a semiregular automorphism of order tending to infinity with n. We prove that there is one of order greater than 2.