Determining the hamilton-connectedness of certain vertex-transitive graphs

Hamilton cycles in dense vertex-transitive graphs

Vertex-Transitive Graphs Of Prime-Squared Order Are Hamilton-Decomposable

We prove that all connected vertex-transitive graphs of order p, p a prime, can be decomposed into Hamilton cycles.

Hamilton cycles and paths in vertex-transitive graphs - Current directions

In this article current directions in solving Lovász’s problem about the existence of Hamilton cycles and paths in connected vertex-transitive graphs are given. © 2009 Elsevier B.V. All rights reserved. 1. Historical motivation In 1969, Lovász [59] asked whether every finite connected vertex-transitive graph has a Hamilton path, that is, a simple path going through all vertices, thus tying toge...

Vertex-transitive graphs that have no Hamilton decomposition

It is shown that there are infinitely many connected vertex-transitive graphs that have no Hamilton decomposition, including infinitely many Cayley graphs of valency 6, and including Cayley graphs of arbitrarily large valency.

Vertex-transitive CIS graphs

A CIS graph is a graph in which every maximal stable set and every maximal clique intersect. A graph is well-covered if all its maximal stable sets are of the same size, co-well-covered if its complement is well-covered, and vertex-transitive if, for every pair of vertices, there exists an automorphism of the graph mapping one to the other. We show that a vertex-transitive graph is CIS if and o...