期刊
JOURNAL OF COMBINATORIAL THEORY SERIES A
卷 155, 期 -, 页码 180-189出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcta.2017.11.006
关键词
Intersecting families; Erdos-Ko-Rado theorem; Hilton-Milner theorem; Diversity; Regular bipartite graphs
类别
资金
- [RNF 16-11-10014]
- Russian Science Foundation [16-11-10014] Funding Source: Russian Science Foundation
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. Our approach is based on the use of regular bipartite graphs. These graphs are quite often used in Extremal Set Theory problems, however, the approach we develop proves to be particularly fruitful. (C) 2017 Elsevier Inc. All rights reserved.
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