A sufficient condition for a pair of sequences to be bipartite graphic
Grant Cairns, Stacey Mendan, Yuri Nikolayevsky
TL;DR
This paper provides a new sufficient condition based on sequence lengths and extremal elements for determining when two integer sequences can be realized as degree sequences of a bipartite graph.
Contribution
It introduces a novel criterion that simplifies verifying bipartite graphicality using only sequence lengths and extremal values.
Findings
The condition is sufficient for bipartite graphicality.
It depends solely on sequence lengths and largest/smallest elements.
The criterion can be applied to efficiently test bipartite degree sequences.
Abstract
We present a sufficient condition for a pair of finite integer sequences to be degree sequences of a bipartite graph, based only on the lengths of the sequences and their largest and smallest elements.
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