Let , and F . Let  be a (k-uniform) matching of size m, if are pairwise disjoint. The matching number is the maximal size of matching which is a subset of F . Note that the condition reduces to  being an intersecting family. A natural idea is to generalize the definition of the matching number so that the intersection family is extended to the t-intersection family. A (k-uniform) t-matching of size m is the set family ,  such that  for any . Denote the maximal size of t-matching which is a subset of  by  (the t-matching number of  ). Notice that  for . And  the condition reduces to  being a t-intersecting family. Let F  with s. We determined for  and n is sufficiently large. Notice that it is known as Erdős matching conjecture when . Furthermore, we gave a related stability theorem and a generalization of HM-form theorem for Erdős matching conjecture to t-matching number. This is joint work with Mei Lu and Haixiang Zhang.

曹梦雨, 中国人民大学讲师, 2020年6月在北京师范大学取得理学博士学位. 2020年9月至2022年9月在清华大学进行博士后研究工作. 研究兴趣为极值图论和代数组合学, 在 J. Combin. Theory Ser A，SIAM J. Discrete Math., European J. Combin. 等期刊发表 SCI 学术论文10余篇，主持国家青年基金一项。