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PROBLEMS AND RESULTS ON 3CHROMATIC HYPERGRAPHS AND SOME RELATED QUESTIONS
 COLLOQUIA MATHEMATICA SOCIETATIS JANOS BOLYAI 10. INFINITE AND FINITE SETS, KESZTHELY (HUNGARY)
, 1973
"... A hypergraph is a collection of sets. This paper deals with finite hypergraphs only. The sets in the hypergraph are called edges, the elements of these edges are points. The degree of a point is the number of edges containing it. The hypergraph is runiform if every edge has r points. A hypergraph i ..."
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surprisingly strict properties on 3chromatic hypergraphs. 6 0 9The reason why we relate these two properties with chromatic number is the following trivial observation: If a hypergraph has chromatic number> 3 with exactly one common point. then it has two edges Let Mk (r) be the minimum number of edges
The chromatic number of comparability 3–hypergraphs
"... Beginning with the concepts of orientation for a 3–hypergraph and transitivity for an oriented 3–hypergraph, it is natural to study the class of comparability 3–hypergraphs (those that can be transitively oriented). In this work we show three different behaviors in respect to the relationship betwee ..."
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between the chromatic number and the clique number of a comparability 3–hypergraph, this is in contrast with the fact that a comparability simple graph is a perfect graph.
On a problem of Erdős and Lovász on coloring nonuniform hypergraphs
, 2008
"... Let f(r) = minH F ∈E(H) 1 2 F  , where H ranges over all 3chromatic hypergraphs with minimum edge cardinality r. ErdősLovász (1975) conjectured f(r) → ∞ as r → ∞. This conjecture was proved by Beck in 1978. Here we show a new proof for this conjecture with a better lower bound: 1 ..."
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Let f(r) = minH F ∈E(H) 1 2 F  , where H ranges over all 3chromatic hypergraphs with minimum edge cardinality r. ErdősLovász (1975) conjectured f(r) → ∞ as r → ∞. This conjecture was proved by Beck in 1978. Here we show a new proof for this conjecture with a better lower bound: 1
Dimension, Graph and Hypergraph Coloring
 ORDER
, 2000
"... There is a natural way to associate with a poset P a hypergraph HP , called the hypergraph of incomparable pairs, so that the dimension of P is the chromatic number of HP . The ordinary graph GP of incomparable pairs determined by the edges in HP of size 2 can have chromatic number substantially ..."
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There is a natural way to associate with a poset P a hypergraph HP , called the hypergraph of incomparable pairs, so that the dimension of P is the chromatic number of HP . The ordinary graph GP of incomparable pairs determined by the edges in HP of size 2 can have chromatic number
List coloring hypergraphs
"... Let H be a hypergraph and let Lv: v ∈ V (H) be sets; we refer to these sets as lists and their elements as colors. A list coloring of H is an assignment of a color from Lv to each v ∈ V (H) in such a way that every edge of H contains a pair of vertices of different colors. The hypergraph H is klist ..."
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. On the other hand there exist dregular threeuniform linear hypergraphs with list chromatic number at most log3 d + 3. This leaves the question open as to the existence of such hypergraphs with list chromatic number o(log d) as d → ∞. 1
On Planar Mixed Hypergraphs
 Electronic J. Combin
"... A mixed hypergraph H is a triple (V,C, D)whereV is its vertex set and C and D are families of subsets of V , Cedges and Dedges. A mixed hypergraph is a bihypergraph i# C = D. A hypergraph is planar if its bipartite incidence graph is planar. A vertex coloring of H is proper if ea ..."
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Cited by 9 (2 self)
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edges of size two is twocolorable. We describe a polynomialtime algorithm to decide whether the lower chromatic number of a planar mixed hypergraph equals two. We prove that it is NPcomplete to find the upper chromatic number of a mixed hypergraph even for 3uniform planar bihypergraphs. In order
The Chromatic Numbers of Random Hypergraphs
 Random Struct. Alg
, 1998
"... : For a pair of integers 1### r, the #chromatic number of an runiform Z. hypergraph H# V, E is the minimal k, for which there exists a partition of V into subsets ## T,...,T such that e#T ## for every e#E. In this paper we determine the asymptotic 1 ki Z. behavior of the #chromatic number of t ..."
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: For a pair of integers 1### r, the #chromatic number of an runiform Z. hypergraph H# V, E is the minimal k, for which there exists a partition of V into subsets ## T,...,T such that e#T ## for every e#E. In this paper we determine the asymptotic 1 ki Z. behavior of the #chromatic number
Coloring simple hypergraphs
, 2008
"... Fix an integer k ≥ 3. A kuniform 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 kuniform hypergraph H with maximum degree ∆ has chromatic number satisfying χ(H) < c ( ) 1 k−1 log ∆ This implies a c ..."
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Fix an integer k ≥ 3. A kuniform 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 kuniform hypergraph H with maximum degree ∆ has chromatic number satisfying χ(H) < c ( ) 1 k−1 log ∆ This implies a
COLOURINGS OF CONFIGURATIONS AS MIXED HYPERGRAPHS
"... This talk will discuss some first results on the upper chromatic number of configurations.The upper chromatic number is concerned with a relatively new concept of vertex colouring of certain hypergraphs. Configurations belong to the oldest known hypergraphs defined already in the 19th century. In ..."
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This talk will discuss some first results on the upper chromatic number of configurations.The upper chromatic number is concerned with a relatively new concept of vertex colouring of certain hypergraphs. Configurations belong to the oldest known hypergraphs defined already in the 19th century
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