The Chromatic Number of Kneser Hypergraphs

@inproceedings{Frankl1986TheCN,
  title={The Chromatic Number of Kneser Hypergraphs},
  author={Peter Frankl and L{\'a}szl{\'o} Lov{\'a}sz},
  year={1986}
}
Suppose the r-subsets of an n-element set are colored by t colors. THEOREM 1.1. IJ n ~ (t l)(k 1) + k . r, then there are k pairwise disjoint r-sets having the same color. This was conjectured by Erdos [El in 1973. Let T(n, r, s) denote the 'lUran number for s-uniform hypergraphs (see §1). THEOREM 1.3. IJe > 0, t ~ (1-e)T(n,r,s)/(k-1), andn > no(e,r,s,k), then there are k r-sets At, A2, .. . , Ak having the same color such that IAi n Ajl < s Jor all 1 ~ i < j ~ k. IJ s = 2, e can be omitted… CONTINUE READING
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Showing 1-9 of 9 references

Borsuk , On the embedding of systems of compacts in simplicial complexes , Fund

K. Bo
Proc . Cambridge Philos . Soc . • 1976

On complete subgraphs of different orders, Math

B. Bollobas
Proc. Cambridge Philos. Soc • 1976

On a graph problem of Turan

T. Nemetz Katona, M. Simonovits
J . Combin . Theory Ser . A • 1973

Modern algebraic topology

D. G. Bourgin
Macmillan, New York; Collier-Macmillan, London • 1963

On the embedding of systems of compacts in simplicial complexes

K. Borsuk
Fund. Math • 1948

On an extremal problem in graph theory, Mat

P. Turan
Fiz. Lapok • 1941

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