AN EXISTENCE THEOREM OF PERFECT MATCHING ON k-PARTITE k-UNIFORM HYPERGRAPHS VIA DISTANCE SPECTRAL RADIUS

Let n1, n2, ... , nk be integers and V1, V2, ... , Vk be disjoint vertex sets with |Vi| = ni for each i = 1, 2, ... , k. A k-partite k-uniform hypergraph on vertex classes V1, V2, ... , Vk is defined to be the k-uniform hypergraph whose edge set consists of the k-element subsets S of V1 boolean OR V2 boolean OR center dot center dot center dot boolean OR Vk such that |S boolean AND Vi| = 1 for all i = 1, 2, ... , k. We say that it is balanced if n1 = n2 = center dot center dot center dot = nk. 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].