Please use this identifier to cite or link to this item: https://research.matf.bg.ac.rs/handle/123456789/602
Title: Formalizing Frankl's conjecture: FC-families
Authors: Marić, Filip 
Živković, Miodrag
Vučković, Bojan
Affiliations: Informatics and Computer Science 
Issue Date: 17-Aug-2012
Related Publication(s): International Conference on Intelligent Computer Mathematics CICM 2012
Journal: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Abstract: 
The Frankl's conjecture, formulated in 1979. and still open, states that in every family of sets closed for unions there is an element contained in at least half of the sets. FC-families are families for which it is proved that every union-closed family containing them satisfies the Frankl's condition (e.g., in every union-closed family that contains a one-element set a, the element a is contained in at least half of the sets, so families of the form a are the simplest FC-families). FC-families play an important role in attacking the Frankl's conjecture, since they enable significant search space pruning. We present a formalization of the computer assisted approach for proving that a family is an FC-family. Proof-by-computation paradigm is used and the proof assistant Isabelle/HOL is used both to check mathematical content, and to perform (verified) combinatorial searches on which the proofs rely. FC-families known in the literature are confirmed, and a new FC-family is discovered. © 2012 Springer-Verlag.
URI: https://research.matf.bg.ac.rs/handle/123456789/602
ISBN: 9783642313738
ISSN: 03029743
DOI: 10.1007/978-3-642-31374-5_17
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