Embeddings of cartesian products of nearly bipartite graphs

Abstract

Surgical techniques are often effective in constructing genus embeddings of Cartesian products of bipartite graphs. In this paper we present a general construction that is "close" to a genus embedding for Cartesian products, where each factor is "close" to being bipartite. In specializing this to repeated Cartesian products of odd cycles, we are able to obtain asymptotic results in connection with the genus parameter for finite abelian groups.