منابع مشابه
Strong Colorings of Hypergraphs
A strong vertex coloring of a hypergraph assigns distinct colors to vertices that are contained in a common hyperedge. This captures many previously studied graph coloring problems. We present nearly tight upper and lower bound on approximating general hypergraphs, both offline and online. We then consider various parameters that make coloring easier, and give a unified treatment. In particular...
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We discuss the properties of uniform hypergraphs which have precisely one partition (i.e., a unique coloring apart from permutation of the colors) under the condition that in each edge, there exist three vertices which belong to precisely two classes of the partition. In particular, we investigate the relation between unique colorability, number of colors, and the cardinalities of color classes.
متن کاملGreedy colorings of uniform hypergraphs
We give a very short proof of an Erdős conjecture that the number of edges in a non-2-colorable n-uniform hypergraph is at least f(n)2, where f(n) goes to infinity. Originally it was solved by József Beck in 1977, showing that f(n) at least c log n. With an ingenious recoloring idea he later proved that f(n) ≥ cn. Here we prove a weaker bound on f(n), namely f(n) ≥ cn. Instead of recoloring a r...
متن کاملPartial Colorings of Unimodular Hypergraphs
Combinatorial discrepancy theory asks for vertex-colorings of hypergraphs such that all hyperedges contain all colors in (as good as possible) equal quantity. Unimodular hypergraphs are good in this sense: They (and all their induced subhypergraphs as well) can be two-colored in a way that in each hyperedge the number of vertices in one color deviates from that in the other color by at most one...
متن کاملKneser 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...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2019
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2019.01.011