منابع مشابه
Coloring Sparse Hypergraphs
Fix k ≥ 3, and let G be a k-uniform hypergraph with maximum degree ∆. Suppose that for each l = 2, . . . , k − 1, every set of l vertices of G is in at most ∆ k−l k−1 /f edges. Then the chromatic number of G is O(( ∆ log f ) 1 k−1 ). This extends results of Frieze and the second author [10] and Bennett and Bohman [2]. A similar result is proved for 3-uniform hypergraphs where every vertex lies ...
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...
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 کاملColoring H-free hypergraphs
Fix r ≥ 2 and a collection of r-uniform hypergraphs H. What is the minimum number of edges in an H-free r-uniform hypergraph with chromatic number greater than k? We investigate this question for various H. Our results include the following: • An (r, l)-system is an r-uniform hypergraph with every two edges sharing at most l vertices. For k sufficiently large, there is an (r, l)-system with chr...
متن کاملColoring 2-Intersecting Hypergraphs
A hypergraph is 2-intersecting if any two edges intersect in at least two vertices. Blais, Weinstein and Yoshida asked (as a first step to a more general problem) whether every 2-intersecting hypergraph has a vertex coloring with a constant number of colors so that each hyperedge has at least min{|e|, 3} colors. We show that there is such a coloring with at most 5 colors (which is best possible...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2016
ISSN: 0895-4801,1095-7146
DOI: 10.1137/140995805