Recent trends and future directions in vertex-transitive graphs

Authors

  • Klavdija Kutnar University of Primorska
  • Dragan Marušič University of Ljubljana and University of Primorska, Slovenia

DOI:

https://doi.org/10.26493/1855-3974.81.679

Keywords:

vertex-transitive graph, arc-transitive graph, half-arc-transitive graph, Hamilton cycle, Hamilton path, semiregular group, (im)primitive group

Abstract

A graph is said to be vertex-transitive if its automorphism group acts transitively on the vertex set. Some recent developments and possible future directions regarding two famous open problems, asking about existence of Hamilton paths and existence of semiregular automorphisms in vertex-transitive graphs, are discussed, together with some recent results on arc-transitive graphs and half-arc-transitive graphs, two special classes of vertex-transitive graphs that have received particular attention over the last decade.

Published

2008-08-21

Issue

Section

Special Issue Bled'07 – Part 2