On the existence of tripartite graphs and n-partite graphs

On the existence of tripartite graphs and n-partite graphs

A sequence of nonnegative integers is said to be graphic if it is the degree sequence of a simple graph , and such a graph is called a realization of . In this article, we generalize Gale and Ryser’s theorem and give the sufficient condition and necessary condition for a triple to be realized by a t...

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Veröffentlicht in:Open mathematics (Warsaw, Poland) Poland), 2024-12, Vol.22 (1), p.264-274
Hauptverfasser: Guo, Jiyun, Li, Haiyan, Zhang, Yuqin, Liu, Lingling, Fu, Miao
Format: Artikel
Sprache:eng
Schlagworte:
05C07
Graphs
monotonous degree condition
n-partite graphs
partite graphs
tripartite graphs
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Zusammenfassung:A sequence of nonnegative integers is said to be graphic if it is the degree sequence of a simple graph , and such a graph is called a realization of . In this article, we generalize Gale and Ryser’s theorem and give the sufficient condition and necessary condition for a triple to be realized by a tripartite graph. Not only that, we also give another stronger monotonous degree condition.
ISSN:2391-5455
2391-5455
DOI:10.1515/math-2024-0093