Recent trends and future directions in vertex-transitive graphs

Klavdija Kutnar, Dragan Marušič

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.

Keywords


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

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

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications