Chain Intersecting Families |
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Authors: | Attila Bernáth Dániel Gerbner |
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Institution: | 1. Department of Operations Research, E?tv?s University, Pázmány P. s. 1/C, Budapest, Hungary, H-1117 2. Department of Information Systems, E?tv?s University, Pázmány P. s. 1/C, Budapest, Hungary, H-1117
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Abstract: | Let
be a family of subsets of an n-element set.
is called (p,q)-chain intersecting if it does not contain chains
and
with
. The maximum size of these families is determined in this paper. Similarly to the p = q = 1 special case (intersecting families) this depends on the notion of r-complementing-chain-pair-free families, where r = p + q − 1. A family
is called r-complementing-chain-pair-free if there is no chain
of length r such that the complement of every set in
also belongs to
. The maximum size of such families is also determined here and optimal constructions are characterized.
The first author is a member of the Egerváry Research Group (EGRES). Research is supported by OTKA grants T 037547 and TS
049788, by European MCRTN Adonet, Contract Grant No. 504438 and by the Egerváry Research Group of the Hungarian Academy of
Sciences.
The work of the second author was partially supported by the Hungarian National Foundation for Scientific Research (OTKA),
grant numbers T037846 and NK62321. |
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Keywords: | Extremal family Disjoint chains Chain-intersecting family Complementing-chain-pair-free family |
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