A complete characterization of graphic sequences with a Z3-connected realization. (January 2016) - Dai, Xiang-Yu; Yin, Jian-Hua
Abstract: A non-increasing sequence π = ( d 1, d 2, …, d n ) 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 Z 3 be a cyclic group of order three. If π has a realization G which is Z 3 -connected, then π has a Z 3 - connected realization G . Yang et al. (2014) proposed the following problem: Characterize all graphic sequences π realizable by a Z 3 -connected graph. In this paper, we solve this problem completely and present a complete characterization of graphic sequences with a Z 3 -connected realization.