Accola theorem on hyperelliptic graphs

Abstract

In this paper, we prove the following theorem: If a graph X is a degree 2 (unramified) covering of a hyperelliptic graph of genus g ≥ 2, then X is γ-hyperelliptic for some γ ≤ g−1 2. This is a discrete analogue of the corresponding theorem for Riemann surfaces. The Bass-Serre theory of coverings of graphs of groups is employed to get the main result.