An extremal problem for set families generated with the union and symmetric difference operations
نویسندگان
چکیده
منابع مشابه
Geodesics in Graphs, an Extremal Set Problem, and Perfect Hash Families
A set U of vertices of a graph G is called a geodetic set if the union of all the geodesics joining pairs of points of U is the whole graph G. One result in this paper is a tight lower bound on the minimum number of vertices in a geodetic set. In order to obtain that result, the following extremal set problem is solved. Find the minimum cardinality of a collection S of subsets of 1⁄2n 1⁄4 f1; 2...
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15 صفحه اولShattering-extremal set systems from Sperner families
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We give a quadratic O(|X|) space representation based on a canonical tree for any subset family F ⊆ 2 holding the closure under union and difference of overlapping members. The cardinal of F is potentially in O(2), and its size higher. As far as we know this is the first representation theorem for such families. As an application of this framework we obtain a uniqueness decomposition theorem on...
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ژورنال
عنوان ژورنال: Journal of Combinatorics
سال: 2012
ISSN: 2156-3527,2150-959X
DOI: 10.4310/joc.2012.v3.n4.a4