Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6871344 | Discrete Applied Mathematics | 2018 | 7 Pages |
Abstract
Let S=(a1,â¦,am;b1,â¦,bn), where a1,â¦,am and b1,â¦,bn are two nonincreasing sequences of nonnegative integers. The pair S=(a1,â¦,am;b1,â¦,bn) is said to be a bigraphic pair if there is a simple bipartite graph G=(XâªY,E) such that a1,â¦,am and b1,â¦,bn are the degrees of the vertices in X and Y, respectively. Let A be an (additive) Abelian group. We define Ï(A,m,n) to be the minimum integer k such that every bigraphic pair S=(a1,â¦,am;b1,â¦,bn) with am,bnâ¥2 and Ï(S)=a1+â¯+amâ¥k has an A-connected realization. In this paper, we determine the values of Ï(A,m,n) for |A|=k and mâ¥nâ¥2, where kâ¥5 is an odd integer.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Jing-Xin Guan, Jian-Hua Yin,