Elsevier

Discrete Mathematics

Volume 247, Issues 1–3, 28 March 2002, Pages 255-259
Discrete Mathematics

Note
Notes on Chvátal's conjecture

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Abstract

Using Kleitman's lemma and results of Schönheim and Miklós it is shown that if w(D)=|D|/2, then every maximum-sized intersecting family in D contains all base elements of D. Then, the converse of this statement is conjectured and shown that this is equivalent to that of Chvátal.

Keywords

Finite set
Downset
Intersecting family

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1

Present address: Department of Mathematics, Nanjing University, Nanjing 210093, People's Republic of China.