Families of Sets with Intersecting Clusters

William Y. C. Chen, Jiuqiang Liu, Larry X. W. Wang

A family of $k$-subsets $A_1,A_2,...,A_d$ on $[n]=\{1,2,...,n\}$ is called a $(d,c)$-cluster if the union $A_1\cup A_2\cup ...\cup A_d$ contains at most $ck$ elements with $…