منابع مشابه
Coloring simple hypergraphs
Fix an integer k ≥ 3. A k-uniform hypergraph is simple if every two edges share at most one vertex. We prove that there is a constant c depending only on k such that every simple k-uniform hypergraph H with maximum degree ∆ has chromatic number satisfying χ(H) < c ( ∆ log ∆ ) 1 k−1 . This implies a classical result of Ajtai-Komlós-Pintz-Spencer-Szemerédi and its strengthening due to Duke-Lefman...
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We study the problem of constructing a (near) uniform random proper q-coloring of a simple k-uniform hypergraph with n vertices and maximum degree ∆. (Proper in that no edge is mono-colored and simple in that two edges have maximum intersection of size one). We show that if for some α < 1 we have ∆ ≥ n and q ≥ ∆ then Glauber dynamics will become close to uniform in O(n log n) time from a random...
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Let m∗(n) be the minimum number of edges in an n-uniform simple hypergraph that is not two colorable. We prove that m∗(n) = Ω(4n/ ln(n)). Our result generalizes to r-coloring of b-simple uniform hypergraphs. For fixed r and b we prove that a maximum vertex degree in b-simple n-uniform hypergraph that is not r-colorable must be Ω(rn/ ln(n)). By trimming arguments it implies that every such graph...
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We study the problem of constructing a (near) uniform random proper q-coloring of a simple k-uniform hypergraph with n vertices and maximum degree ∆. (Proper in that no edge is mono-colored and simple in that two edges have maximum intersection of size one). We show that if q ≥ max { Ck log n, 500k 3∆1/(k−1) } then the Glauber Dynamics will become close to uniform in O(n log n) time, given a ra...
متن کاملOnline coloring of hypergraphs
We give a tight bound on randomized online coloring of hypergraphs. The bound holds even if the algorithm knows the hypergraph in advance (but not the ordering in which it is presented). More specifically, we show that for any n and k, there is a 2colorable k-uniform hypergraph on n vertices for which any randomized online coloring uses Ω(n/k) colors in expectation. 1 Online Hypergraph Coloring...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2013
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2013.09.003