An existence theorem of perfect matching on $k$-partite $k$-uniform hypergraphs via distance spectral radius

Document Type : Research Paper

Authors

Department of Mathematics and Statistics, Qinghai Normal University, Xining, China

Abstract

Let $n_1, n_2,\ldots,n_k$ be integers and $V_1, V_2,\ldots,V_k$ be disjoint vertex sets with $|V_i|=n_i$ for each $i= 1, 2,\ldots,k$. A $k$-partite $k$-uniform hypergraph on vertex classes $V_1, V_2,\ldots,V_k$ is defined to be the $k$-uniform hypergraph whose edge set consists of the $k$-element subsets $S$ of $V_1 \cup V_2 \cup \cdots \cup V_k$ such that $|S\cap V_i|=1$ for all $i= 1, 2,\ldots,k$. We say that it is balanced if $n_1=n_2=\cdots=n_k$. In this paper, we give a distance spectral radius condition to guarantee the existence of perfect matching in $k$-partite $k$-uniform hypergraphs, this result generalize the result of Zhang and Lin  [Perfect matching and distance spectral radius in graphs and bipartite graphs, Discrete Appl. Math., 304 (2021) 315-322].

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References

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Transactions on Combinatorics
Volume 13, Issue 4 - Serial Number 4
December 2024
Pages 377-385

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History

  • Receive Date: 06 June 2023
  • Revise Date: 25 October 2023
  • Accept Date: 29 October 2023
  • Published Online: 01 December 2024

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