Affiliation:
1. Data Science Institute Shandong University Jinan China
2. School of Mathematics and Statistics and Center for Applied Mathematics Beijing Institute of Technology Beijing China
3. Department of Mathematics University of Rhode Island Kingston Rhode Island USA
Abstract
AbstractFor integers and , we show that for every , there exists such that the union of ‐uniform hypergraph on vertices with minimum codegree at least and a binomial random ‐uniform hypergraph with on the same vertex set contains the power of a tight Hamilton cycle with high probability. Moreover, a construction shows that one cannot take , where is a constant. Thus the bound on is optimal up to the value of and this answers a question of Bedenknecht, Han, Kohayakawa, and Mota.
Funder
China Postdoctoral Science Foundation
National Natural Science Foundation of China
Natural Science Foundation of Shandong Province
Simons Foundation
Subject
Applied Mathematics,Computer Graphics and Computer-Aided Design,General Mathematics,Software