An upper bound for the size of a k-uniform intersecting family with covering number k

摘要

Let r(k) denote the maximum number of edges in a k-uniform intersecting family with covering number k. Erdos and Lovasz proved that [k!(e - 1)] <= r(k) <= k(k). Frankl, Ota, and Tokushige improved the lower bound to r(k) >= (k/2)(k-1), and Tuza improved the upper bound to r(k) <= (1 - e(-1) + o(1))k(k). We establish that r(k) <= (1 + o(1))k(k-1). (C) 2016 Elsevier Inc. All rights reserved.