Geodesic
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)
Ars Mathematica Contemporanea, Tome 19 (2020) no. 1, pp. 1-15.

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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.
DOI : 10.26493/1855-3974.2163.5df
Keywords: Vertex-transitive graph, Hamilton cycle, automorphism group, orbital graph 
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Shaofei Du; Klavdija Kutnar; Dragan Marušič. 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). Ars Mathematica Contemporanea, Tome 19 (2020) no. 1, pp. 1-15. doi : 10.26493/1855-3974.2163.5df. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2163.5df/

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