منابع مشابه
On The Chromatic Number of Geometric Hypergraphs
A finite family R of simple Jordan regions in the plane defines a hypergraph H = H(R) where the vertex set of H is R and the hyperedges are all subsets S ⊂ R for which there is a point p such that S = {r ∈ R|p ∈ r}. The chromatic number of H(R) is the minimum number of colors needed to color the members of R such that no hyperedge is monochromatic. In this paper we initiate the study of the chr...
متن کاملOn the Chromatic Number of Kneser Hypergraphs
We give a simple and elementary proof of Kř́ıž’s lower bound on the chromatic number of the Kneser r-hypergraph of a set system S.
متن کاملOn The Choice Number Of Random Hypergraphs
We generalize the notion of choice number from graphs to hypergraphs and estimate the sharp order of magnitude of the choice number of random hypergraphs. It turns out that the choice number and the chromatic number of a random hypergraph have the same order of magnitude, almost surely. Our result implies an earlier bound on the chromatic number of random hypergraphs, proved by Schmidt [Sch] us...
متن کاملOn the Size-Ramsey Number of Hypergraphs
The size-Ramsey number of a graph G is the minimum number of edges in a graph H such that every 2-edge-coloring of H yields a monochromatic copy of G. Size-Ramsey numbers of graphs have been studied for almost 40 years with particular focus on the case of trees and bounded degree graphs. We initiate the study of size-Ramsey numbers for k-uniform hypergraphs. Analogous to the graph case, we cons...
متن کاملOn the Fractional Covering Number of Hypergraphs
The fractional covering number r* of a hypergraph H (V, E) is defined to be the minimum possible value of ,, v t(x) where ranges over all functions t: V which satisfy ,xe t(x) >= for all edges e e E. In the case of ordinary graphs G, it is known that 2r*(G) is always an integer. By contrast, it is shown (among other things) that for any rational p/q >= 1, there is a 3-uniform hypergraph H with-...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2017
ISSN: 0364-9024,1097-0118
DOI: 10.1002/jgt.22115