Mixed hypergraphs and other coloring problems
نویسندگان
چکیده
منابع مشابه
Coloring Mixed Hypergraphs: from Combinatorics to Philosophy∗
We survey recent results and open problems on the chromatic spectrum, planarity and colorability of mixed hypergraphs and their relations to such categories of philosophy as identity and difference.
متن کاملGeombinatorial Mixed Hypergraph Coloring Problems
Can you color Rn so that point sets of one sort are never monochromatic, while point sets of another sort always are? If so, how many colors did you use, and can you do the job with more or fewer colors?
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...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2007
ISSN: 0012-365X
DOI: 10.1016/j.disc.2005.11.050