ALMOST PERFECT MATCHINGS IN k-PARTITE k-GRAPHS

作者:Lu, Hongliang*; Wang, Yan; Yu, Xingxing
来源:SIAM Journal on Discrete Mathematics, 2018, 32(1): 522-533.
DOI:10.1137/16M1097948

摘要

The minimum codegree threshold for a perfect matching in a k-graph with n vertices was determined by Rodl, Rucinski, and Szemeredi for the case when n equivalent to 0 (mod k). Recently, Han resolved the remaining cases when n not equivalent to 0 (mod k), establishing a conjecture of Rodl, Rucinski, and Szemeredi. In this paper, we determine the minimum codegree threshold for almost perfect matchings in k-partite k-graphs, answering a question of Rodl and Rucinski.