منابع مشابه
Kneser Colorings of Uniform Hypergraphs
For xed positive integers r, k and ` with ` < r, and an r-uniform hypergraph H, let κ(H, k, `) denote the number of k-colorings of the set of hyperedges of H for which any two hyperedges in the same color class intersect in at least ` vertices. Consider the function KC(n, r, k, `) = maxH∈Hn κ(H, k, `), where the maximum runs over the family Hn of all r-uniform hypergraphs on n vertices. In this...
متن کاملOn generalized Kneser hypergraph colorings
In Ziegler (2002), the second author presented a lower bound for the chromatic numbers of hypergraphs KG sS, “generalized r-uniform Kneser hypergraphs with intersection multiplicities s.” It generalized previous lower bounds by Kř́ıž (1992/2000) for the case s = (1, . . . , 1) without intersection multiplicities, and by Sarkaria (1990) for S = ([n] k ) . Here we discuss subtleties and difficulti...
متن کاملHypergraphs with many Kneser colorings
For fixed positive integers r, k and ` with 1 ≤ ` < r and an r-uniform hypergraph H, let κ(H, k, `) denote the number of k-colorings of the set of hyperedges of H for which any two hyperedges in the same color class intersect in at least ` elements. Consider the function KC(n, r, k, `) = maxH∈Hn κ(H, k, `), where the maximum runs over the family Hn of all r-uniform hypergraphs on n vertices. In...
متن کاملOn Fall Colorings of Kneser Graphs
A fall k-coloring of a graph G is a proper k-coloring of G such that each vertex of G sees all k colors on its closed neighborhood. In this note, we characterize all fall colorings of Kneser graphs of type KG(n, 2) for n ≥ 2 and study some fall colorings of KG(n,m) in some special cases and introduce some bounds for fall colorings of Kneser graphs.
متن کاملFrom the Kneser-Poulsen conjecture to ball-polyhedra
A very fundamental geometric problem on finite systems of spheres was independently phrased by Kneser (1955) and Poulsen (1954). According to their well-known conjecture if a finite set of balls in Euclidean space is repositioned so that the distance between the centers of every pair of balls is decreased, then the volume of the union (resp., intersection) of the balls is decreased (resp., incr...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1989
ISSN: 0019-2082
DOI: 10.1215/ijm/1255988573