Hamilton compression in Vertex-transitive Graphs

Given a graph $X$ with a Hamilton cycle $C$, the compression factor $\kappa(X,C)$ of $C$ is the order of the largest cyclic subgroup of $C\cap X$, and the Hamilton compression $\kappa(X)$ of $X$ is the maximum of $\kappa(X,C)$ 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.