Regular bipartite graphs and intersecting families

摘要

In this paper we present a simple unifying approach to prove several statements about intersecting and cross-intersecting families, including the Erdos-Ko-Rado theorem, the Hilton-Milner theorem, a theorem due to Frankl concerning the size of intersecting families with bounded maximal degree, and versions of results on the sum of sizes of non-empty cross intersecting families due to Frankl and Tokushige. Several new stronger results are also obtained.