Open Mathematics (Dec 2024)

On the existence of tripartite graphs and n-partite graphs

  • Guo Jiyun,
  • Li Haiyan,
  • Zhang Yuqin,
  • Liu Lingling,
  • Fu Miao

DOI
https://doi.org/10.1515/math-2024-0093
Journal volume & issue
Vol. 22, no. 1
pp. 264 – 274

Abstract

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A sequence α\alpha of nonnegative integers is said to be graphic if it is the degree sequence of a simple graph GG, and such a graph GG is called a realization of α\alpha . 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.

Keywords