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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.