Abstract
Frankl’s union-closed sets conjecture states that in every finite union-closed set of sets, there is an element that is contained in at least half of the member-sets (provided there are at least two members). The conjecture has an equivalent formulation in terms of graphs: In every bipartite graph with least one edge, both colour classes contain a vertex belonging to at most half of the maximal stable sets.
We prove that, for every fixed edge-probability, almost every random bipartite graph almost satisfies Frankl’s conjecture.
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© 2013 Scuola Normale Superiore Pisa
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Bruhn, H., Schaudt, O. (2013). The union-closed sets conjecture almost holds for almost all random bipartite graphs. In: Nešetřil, J., Pellegrini, M. (eds) The Seventh European Conference on Combinatorics, Graph Theory and Applications. CRM Series, vol 16. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-475-5_13
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DOI: https://doi.org/10.1007/978-88-7642-475-5_13
Publisher Name: Edizioni della Normale, Pisa
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Online ISBN: 978-88-7642-475-5
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