An extremal problem on bigraphic pairs with an A-connected realization

作者：Yin, Jian-Hua^*

来源：Discrete Mathematics, 2016, 339(8): 2018-2026.

DOI：10.1016/j.disc.2016.02.014

• Bigraphic pairs
• Z(3)-connected realization
• Group connectivity

Let S = (a(1),...,a(m); b(1),..., b(n)), where a(1),..., a(m) and b(1),...,b(n) are two nonincreasing sequences of nonnegative integers. The pair S = (a(1),..., a(m); b(1),..., b(n)) is said to be a bigraphic pair if there is a simple bipartite graph G = (X boolean OR Y, E) such that a(1),..., a(m) and b(1),..., b(n) are the degrees of the vertices in X and Y, respectively. Let A be an (additive) Abelian group. We define sigma (A, m, n) to be the minimum integer k such that every bigraphic pair S = (a(1),...,a(m); b(1),..., b(n)) with a(m), b(n) >= 2 and sigma(S) = a(1)+ ... + a(m) >= k has an A-connected realization. In this paper, we determine the values of sigma(Z(3), m, m) for m >= 4.

• 出版日期2016-8-6
• 单位海南大学