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

Let n_۱, n_۲,\ldots,n_k be integers and V_۱, V_۲,\ldots,V_k be disjoint vertex sets with |V_i|=n_i for each i= ۱, ۲,\ldots,k. A k-partite k-uniform hypergraph on vertex classes V_۱, V_۲,\ldots,V_k is defined to be the k-uniform hypergraph whose edge set consists of the k-element subsets S of V_۱ \cup V_۲ \cup \cdots \cup V_k such that |S\cap V_i|=۱ for all i= ۱, ۲,\ldots,k. We say that it is balanced if n_۱=n_۲=\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., ۳۰۴ (۲۰۲۱) ۳۱۵-۳۲۲].

کلیدواژه ها:

k-uniform k-partite hypergraphs ، Distance spectral radius ، perfect matching