The graph formulation of the union-closed sets conjecture
نویسندگان
چکیده
منابع مشابه
The graph formulation of the union-closed sets conjecture
In 1979 Frankl conjectured that in a finite non-trivial union-closed collection of sets there has to be an element that belongs to at least half the sets. We show that this is equivalent to the conjecture that in a finite non-trivial graph there are two adjacent vertices each belonging to at most half of the maximal stable sets. In this graph formulation other special cases become natural. The ...
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The union-closed sets conjecture states that if a finite family of sets A 6 = {∅} is union-closed, then there is an element which belongs to at least half the sets in A. In 2001, D. Reimer showed that the average set size of a union-closed family, A, is at least 1 2 log2 |A|. In order to do so, he showed that all union-closed families satisfy a particular condition, which in turn implies the pr...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2015
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2014.08.030