#### Abstract

A bisection of a graph G is a balanced bipartite spanning subgraph of G. Given a graphic sequence π, we show that π has a realization G containing a bisection H where degH(v) ≥ b(degG(v)− 1)/2c for all vertices v. This bound is very close to best possible. We use this result to provide evidence for a conjecture of Busch et. al. [1] that if π and π − k are… (More)