Solution to an Extremal Problem on Bigraphic Pairs with a Z3-connected Realization

作     者：Jian Hua YIN Xiang Yu DAI 

作者机构：Department of MathematicsCollege of Information Science and TechnologyHainan UniversityHaikou 570228P.R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2017年第33卷第8期

页      面：1131-1153页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Supported by National Natural Science Foundation of China(Grant No.11561017) Natural Science Foundation of Hainan Province(Grant No.2016CXTD004) 

主　　题：Bigraphic pair Z3-connected realization group connectivity 

摘      要：Let S = （a1,...,am;b1,...,bn）, where a1,...,am and b1,...,bn are two nonincreasing sequences of nonnegative integers. The pair S= （a1,..., am; b1,..., bn） is said to be a bigraphic pair if there is a simple bipartite graph G = （X ∪ Y, E） such that a1,…, am and b1,..., bn are the degrees of the vertices in X and Y, respectively. Let Z3 be the cyclic group of order 3. Define σ（Z3, m, n） to be the minimum integer k such that every bigraphic pair S = （a1,..., am; b1,..., bn） with am, b ≥ 2 and σ（S） = a1 ＋ ... ＋ am ≥ k has a Z3-connected realization. For n = m, Yin [Discrete Math., 339, 2018-2026 （2016）] recently determined the values of σ（Z3,m,m） for m ≥ 4. In this paper, we completely determine the values of σ（Z3, m, n） for m ≥ n ≥4.