منابع مشابه
Complete Kneser Transversals
Let k, d, λ > 1 be integers with d > λ. Let m(k, d, λ) be the maximum positive integer n such that every set of n points (not necessarily in general position) in R has the property that the convex hulls of all k-sets have a common transversal (d − λ)-plane. It turns out that m(k, d, λ) is strongly connected with other interesting problems, for instance, the chromatic number of Kneser hypergraph...
متن کاملCodimension two and three Kneser Transversals
Let k, d, λ > 1 be integers with d > λ and let X ⊂ R be a finite set. A (d−λ)-plane L transversal to the convex hull of all k-sets of X is called Kneser transversal. If in addition L contains (d− λ) + 1 points of X, then L is called complete Kneser transversal. In this paper, we present various results on the existence of (complete) Kneser transversals for λ = 2, 3. In order to do this, we intr...
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We prove an analog of results by Erdős-Ko-Rado and GreenwellLovász by characterising the maximum stable sets in special vertex-transitive subgraphs of powers of complete graphs, and proving that these graphs admit a unique optimal vertex colouring, up to permutation of the coordinates.
متن کاملCommon Transversals
Given t families, each family consisting of s finite sets, we show that if the families “separate points" in a natural way, and if the union of all the sets in all the families contains more than (s+1)t st 1 1 elements, then a common transversal of the t families exists. In case each family is a covering family, the bound is st st 1. Both of these bounds are best possible. This work extends rec...
متن کاملConvex Transversals
We answer the question initially posed by Arik Tamir at the Fourth NYU Computational Geometry Day (March, 1987): “Given a collection of compact sets, can one decide in polynomial time whether there exists a convex body whose boundary intersects every set in the collection?” We prove that when the sets are segments in the plane, deciding existence of the convex stabber is NP-hard. The problem re...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2017
ISSN: 0196-8858
DOI: 10.1016/j.aam.2016.07.004