Combinatorics and Graph Theory


A Lemma on the Minimal Counter-example of Frankl's Conjecture

Authors: Ankush Hore

Frankl's Conjecture, from 1979, states that any finite union-closed family, containing at least one non-empty member set, must have an element which belongs to at least half of the member-sets. In this paper we list out some properties of the hypothetical minimal counter-example to this conjecture. In particular, we discuss the frequency of 3 distinct elements in the minimal counter-example. We also apply these findings to finite bipartite graphs.

Comments: 5 Pages.

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Submission history

[v1] 2018-01-05 21:59:11
[v2] 2018-01-07 11:57:20

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