Hamilton cycles in primitive vertex-transitive graphs of order a product of two primes - the case PSL(2, qsup2) acting on cosets of PGL(2, q) - Du, Shao Fei (Ars mathematica contemporanea, 2020)
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?$(2, q^2)$? on cosets of its subgroup isomorphic to the projective general linear group PGL$(2, q)$ contains a Hamilton cycle.
Keywords: automorphism group; grupa avtomorfizmov; Hamilton cycle; hamiltonski cikel; orbital graph; orbitalni graf; točkovno tranzitiven graf; vertex-transitive graph