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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
Cluster Ensembles  A Knowledge Reuse Framework for Combining Multiple Partitions
 Journal of Machine Learning Research
, 2002
"... This paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings. We first identify several application scenarios for the resultant 'knowledge reuse&ap ..."
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Cited by 603 (20 self)
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This paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings. We first identify several application scenarios for the resultant 'knowledge reuse
The monadic secondorder logic of graphs I. Recognizable sets of Finite Graphs
 Information and Computation
, 1990
"... The notion of a recognizable sef offinite graphs is introduced. Every set of finite graphs, that is definable in monadic secondorder logic is recognizable, but not vice versa. The monadic secondorder theory of a contextfree set of graphs is decidable. 0 19W Academic Press. Inc. This paper begins ..."
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an investigation of the monadic secondorder logic of graphs and of sets of graphs, using techniques from universal algebra, and the theory of formal languages. (By a graph, we mean a finite directed hyperedgelabelled hypergraph, equipped with a sequence of distinguished vertices.) A survey of this research can
Directed Hypergraphs And Applications
, 1992
"... We deal with directed hypergraphs as a tool to model and solve some classes of problems arising in Operations Research and in Computer Science. Concepts such as connectivity, paths and cuts are defined. An extension of the main duality results to a special class of hypergraphs is presented. Algorith ..."
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Cited by 137 (5 self)
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We deal with directed hypergraphs as a tool to model and solve some classes of problems arising in Operations Research and in Computer Science. Concepts such as connectivity, paths and cuts are defined. An extension of the main duality results to a special class of hypergraphs is presented
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.
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
Coloring sparse hypergraphs
"... Fix k ≥ 3, and let G be a kuniform hypergraph with maximum degree ∆. Suppose that for each l = 2,..., k − 1, every set of l vertices of G is in at most k−l k−1 /f edges. Then the chromatic number of G is O( ( ∆log f) 1 k−1). This extends results of Frieze and the second author [10] and Bennett and ..."
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Fix k ≥ 3, and let G be a kuniform hypergraph with maximum degree ∆. Suppose that for each l = 2,..., k − 1, every set of l vertices of G is in at most k−l k−1 /f edges. Then the chromatic number of G is O( ( ∆log f) 1 k−1). This extends results of Frieze and the second author [10] and Bennett
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
Density conditions for panchromatic colourings of hypergraphs
 COMBINATORICA
, 2001
"... Let H=(V,E) be a hypergraph. A panchromatic tcolouring of H is a tcolouring of its vertices such that each edge has at least one vertex of each colour; and H is panchromatically tchoosable if, whenever each vertex is given a list of t colours, the vertices can be coloured from their lists in such ..."
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 + t − 1)/t whenever ∅̸ = F⊆E, and this condition is sharp. This last result dualizes to a sharp sufficient condition for the chromatic index of a hypergraph to equal its maximum degree.
About vertexcritical nonbicolorable hypergraphs
 Austral. J. Combin
, 1994
"... The hypergraphs whose chromatic number is ~ 2 ("bicolorable " hypergraphs) were introduced by E.W. Miller [13] under the name of "setsystems with Property B". This concept appears in Number Theory (see [5], [10]). It is also useful for some problems in positional games and Opera ..."
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and Operations Research (see [3], [4], [7]); different results have been found under the form of inequalities involving the sizes of the edges, the number of vertices, etc... ( see [6], [11], [12]). A nonbicolorable hypergraph which becomes bicolorable when any of its edges is removed is called "
Results 1  10
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