Hamilton cycles in primitive vertex-transitive graphs of order a product of two primes – the case PSL(2, q^2)  acting on cosets of PGL(2, q)

Shaofei Du; Klavdija Kutnar; Dragan Marušič

doi:10.26493/1855-3974.2163.5df

Hamilton cycles in primitive vertex-transitive graphs of order a product of two primes – the case PSL(2, q^2) acting on cosets of PGL(2, q)

Authors

Shaofei Du Capital Normal University, China https://orcid.org/0000-0001-6725-9293
Klavdija Kutnar University of Primorska, Slovenia https://orcid.org/0000-0002-9836-6398
Dragan Marušič University of Primorska, Slovenia and IMFM, Slovenia https://orcid.org/0000-0002-8452-3057

DOI:

https://doi.org/10.26493/1855-3974.2163.5df

Keywords:

Vertex-transitive graph, Hamilton cycle, automorphism group, orbital graph

Abstract

A step forward is made in a long standing Lovász problem regarding hamiltonicity of vertex-transitive graphs by showing that every connected vertex-transitive graph of order a product of two primes arising from the group action of the projective special linear group PSL(2, q²) on cosets of its subgroup isomorphic to the projective general linear group PGL(2, q) contains a Hamilton cycle.

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Published

2020-10-26

Issue

Vol. 19 No. 1 (2020)

Section

Articles

License

Articles in this journal are published under Creative Commons Attribution 4.0 International License
https://creativecommons.org/licenses/by/4.0/