منابع مشابه
Randomly coloring simple hypergraphs
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...
متن کاملRandomly coloring simple hypergraphs with fewer colors
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 کاملRandomly colouring simple hypergraphs
We study the problem of constructing a (near) random proper q-colouring of a simple k-uniform hypergraph with n vertices and maximum degree ∆. (Proper in that no edge is mono-coloured and simple in that two edges have maximum intersection of size one). We give conditions on q,∆ so that if these conditions are satisfied, Glauber dynamics will converge in O(n log n) time from a random (improper) ...
متن کاملColoring 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...
متن کاملMultipass greedy coloring of simple uniform hypergraphs
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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ژورنال
عنوان ژورنال: Information Processing Letters
سال: 2011
ISSN: 0020-0190
DOI: 10.1016/j.ipl.2011.06.001