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On generalized Kneser hypergraph colorings
, 2006
"... In Ziegler (2002), the second author presented a lower bound for the chromatic numbers of hypergraphs KGr sS, “generalized runiform Kneser hypergraphs with intersection multiplicities s. ” It generalized previous lower bounds by Kˇríˇz (1992/2000) for the case s = (1,...,1) without intersection mul ..."
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In Ziegler (2002), the second author presented a lower bound for the chromatic numbers of hypergraphs KGr sS, “generalized runiform Kneser hypergraphs with intersection multiplicities s. ” It generalized previous lower bounds by Kˇríˇz (1992/2000) for the case s = (1,...,1) without intersection
COLORFUL HYPERGRAPHS IN KNESER HYPERGRAPHS
, 2013
"... Using a Zqgeneralization of a theorem of Ky Fan, we extend to Kneser hypergraphs a theorem of Simonyi and Tardos that ensures the existence of multicolored complete bipartite graphs in any proper coloring of a Kneser graph. It allows to derive a lower bound for the local chromatic number of Kneser ..."
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Using a Zqgeneralization of a theorem of Ky Fan, we extend to Kneser hypergraphs a theorem of Simonyi and Tardos that ensures the existence of multicolored complete bipartite graphs in any proper coloring of a Kneser graph. It allows to derive a lower bound for the local chromatic number
Kneser colorings of uniform hypergraphs
"... For fixed positive integers r, k and ℓ with ℓ < r, and an runiform hypergraph H, let κ(H, k, ℓ) denote the number of kcolorings of the set of hyperedges of H for which any two hyperedges in the same color class intersect in at least ℓ vertices. Consider the function KC(n, r, k, ℓ) = max H ∈ Hn ..."
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For fixed positive integers r, k and ℓ with ℓ < r, and an runiform hypergraph H, let κ(H, k, ℓ) denote the number of kcolorings of the set of hyperedges of H for which any two hyperedges in the same color class intersect in at least ℓ vertices. Consider the function KC(n, r, k, ℓ) = max H
HYPERGRAPHS WITH MANY KNESER COLORINGS
"... Abstract. For fixed positive integers r, k and ℓ with 1 ≤ ℓ < r and an runiform hypergraph H, let κ(H, k, ℓ) denote the number of kcolorings of the set of hyperedges of H for which any two hyperedges in the same color class intersect in at least ℓ elements. Consider the function KC(n, r, k, ℓ) ..."
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Abstract. For fixed positive integers r, k and ℓ with 1 ≤ ℓ < r and an runiform hypergraph H, let κ(H, k, ℓ) denote the number of kcolorings of the set of hyperedges of H for which any two hyperedges in the same color class intersect in at least ℓ elements. Consider the function KC(n, r, k, ℓ
On the chromatic number of Kneser hypergraphs
, 2000
"... We give a simple and elementary proof of Kr'iz's lower bound on the chromatic number of the Kneser rhypergraph of a set system S. ..."
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Cited by 5 (1 self)
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We give a simple and elementary proof of Kr'iz's lower bound on the chromatic number of the Kneser rhypergraph of a set system S.
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
On splittable colorings of graphs and hypergraphs
"... The notion of a split coloring of a complete graph was introduced by Erdős and Gyárfás [7] as a generalization of split graphs. In this paper, we offer an alternate interpretation by comparing such a coloring to the classical Ramsey coloring problem via a tworound game played against an adversary. ..."
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The notion of a split coloring of a complete graph was introduced by Erdős and Gyárfás [7] as a generalization of split graphs. In this paper, we offer an alternate interpretation by comparing such a coloring to the classical Ramsey coloring problem via a tworound game played against an adversary
Results 1  10
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3,693