Gergely Harcos: Hamiltonian paths and Ramanujan graphs

Abstract:

In recent joint work with Dániel Soltész, we proved a new upper bound on the maximum number of pairwise $C_{2k}$-creating Hamiltonian paths of $K_n$. For the case of $k>3$, we employed the Ramanujan graphs constructed by Lubotzky-Phillips-Sarnak. The talk will focus on arithmetic features of the proof such as: what are these Ramanujan graphs, and how do we choose their parameters (which are two prime numbers).

For Zoom access please contact Andras Biro (biro.andras[a]renyi.hu).