Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776935 | Discrete Mathematics | 2017 | 6 Pages |
Abstract
Let S=(a1,â¦,am;b1,â¦,bn) be a pair of two nonincreasing sequences of positive integers, that is, a1,â¦,am and b1,â¦,bn are two nonincreasing sequences of positive 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. In this paper, we give a simple sufficient condition for a pair S=(a1,â¦,am;b1,â¦,bn) to be a bigraphic pair. The condition depends only on the lengths of two sequences of the pair and their largest and smallest elements. This result extends a result due to Alon et al. (2010).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Lei Meng, Jian-Hua Yin,