About the upper chromatic number of a co-hypergraph
نویسندگان
چکیده
منابع مشابه
On the upper chromatic number of a hypergraph
We introduce the notion of a of a hypergraph, which is a subset of vertices to be colored so that at least two vertices are of the same color. Hypergraphs with both and are called mixed hypergraphs. The maximal number of colors for which there exists a mixed hypergraph coloring using all the colors is called the upper chromatic number of a hypergraph H and is denoted by X(H). An algorithm for c...
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A mixed hypergraph is a triple H = (X, C,D), where X is the vertex set and each of C, D is a family of subsets of X, the C-edges and D-edges, respectively. A proper k-coloring of H is a mapping c : X → [k] such that each C-edge has two vertices with a common color and each D-edge has two vertices with distinct colors. Upper chromatic number is the maximum number of colors that can be used in a ...
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In a graph, by definition, the weight of a (proper) coloring with positive integers is the sum of the colors. The chromatic sum is the minimum weight, taken over all the proper colorings. The minimum number of colors in a coloring of minimum weight is the cost chromatic number or strength of the graph. We derive general upper bounds for the strength, in terms of a new parameter of representatio...
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The hypergraph product G2H has vertex set V (G) × V (H), and edge set {e × f : e ∈ E(G), f ∈ E(H)}, where × denotes the usual cartesian product of sets. We construct a hypergraph sequence {Gn} for with χ(Gn) → ∞ and χ(Gn2Gn) = 2 for all n. This disproves a conjecture of Berge and Simonovits [2]. On the other hand, we show that if G and H are hypergraphs with infinite chromatic number, then the ...
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We consider the problem of k-colouring a random r-uniform hypergraph with n verticesand cn edges, where k, r, c remain constant as n → ∞. Achlioptas and Naor showed that thechromatic number of a random graph in this setting, the case r = 2, must have one of twoeasily computable values as n→∞. We give a complete generalisation of this result to randomuniform hypergraphs.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2000
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(99)00382-9