Chain Intersecting Families
نویسندگان
چکیده
Let F be a family of subsets of an n-element set. F is called (p,q)-chain intersecting if it does not contain chains A1 ( A2 ( · · · ( Ap and B1 ( B2 ( · · · ( Bq with Ap∩Bq = ∅. 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 F is called r-complementing-chain-pair-free if there is no chain L ⊆ F of length r such that the complement of every set in L also belongs to F . The maximum size of such families is also determined here and optimal constructions are characterized.
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ورودعنوان ژورنال:
- Graphs and Combinatorics
دوره 23 شماره
صفحات -
تاریخ انتشار 2007