Hamilton cycles in dense vertex-transitive graphs

Hamilton cycles in dense vertex-transitive graphs

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-Oriented Hamilton Cycles in Directed Graphs

Let D be a directed graph of order n. An anti-directed Hamilton cycle H in D is a Hamilton cycle in the graph underlying D such that no pair of consecutive arcs in H form a directed path in D. We prove that if D is a directed graph with even order n and if the indegree and the outdegree of each vertex of D is at least 23n then D contains an anti-directed Hamilton cycle. This improves a bound of...

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 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.