Dichotomy Result on 3-Regular Bipartite Non-negative Functions

Abstract

We prove a complexity dichotomy theorem for a class of Holant problems on 3-regular bipartite graphs. Given an arbitrary nonnegative weighted symmetric constraint function \(f = [x_0, x_1, x_2, x_3]\), we prove that the bipartite Holant problem \({\text {Holant}}\left( f\mid (=_3)\right) \) is either computable in polynomial time or #P-hard. The dichotomy criterion on f is explicit.KeywordsDichotomy theoremHolant problemBipartite graph