Hamilton compression in Vertex-transitive Graphs

Given a graph X with a Hamilton cycle C, the compression factor κ(X,C) of C is the order of the largest cyclic subgroup of C∩ X, and the Hamilton compression κ(X) of X is the maximum of κ(X,C) where C runs over all Hamilton cycles in X. Motivated by Gregor, Merino and Mütze generalization of the well-known open problem regarding the existence of vertex-transitive graphs without Hamilton paths/cycles we have recently started to investigate existence of Hamilton cycles, admitting large rotational symmetry, in certain families of vertex-transitive graphs. In this talk I will present the results obtained thus far with a special emphasis given to the importance of the so-called Polycirculant conjecture when investigating Hamilton compression in vertex-transitive graphs. The work discussed in this talk is a joint work with Dragan Marušič and Andriaherimanana Sarobidy Razafimahatratra.