Hamilton cycles in primitive vertex-transitive graphs of order a product of two primes - the case PSL(2, q2) acting on cosets of PGL(2, q)

Abstract

A step forward is made in a long standing Lovasz 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,  q 2 ) on cosets of its subgroup isomorphic to the projective general linear group PGL (2,  q ) contains a Hamilton cycle.