A complete characterization of graphic sequences with a Z3-connected realization

A non-increasing sequence π=(d1,d2,…,dn) of non-negative integers is said to be graphic if it is the degree sequence of a simple graph G on n vertices. We say that G is a realization of π (or π is realizable by G). Let Z3 be a cyclic group of order three. If π has a realization G which is Z3-connected, then π has a Z3-connected realization G. Yang et al. (2014) proposed the following problem: Characterize all graphic sequences π realizable by a Z3-connected graph. In this paper, we solve this problem completely and present a complete characterization of graphic sequences with a Z3-connected realization.