Document Zbl 0498.05048

Intersection theorems with geometric consequences. (English) Zbl 0498.05048

Combinatorica 1, 357-368 (1981).

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MSC:

05C65	Hypergraphs
05A05	Permutations, words, matrices
05C15	Coloring of graphs and hypergraphs
05C35	Extremal problems in graph theory
03E05	Other combinatorial set theory

Keywords:

set intersections

Citations:

Zbl 0342.05018; Zbl 0407.05006

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Full Text: DOI

References:

[1]	L. Babai andP. Frankl, On set intersections,J. Comb. Th. A 28 (1980), 103–105. · Zbl 0432.05002 · doi:10.1016/0097-3165(80)90063-1
[2]	M. Deza, P. Erdos andP. Frankl, Intersection properties of systems of finite sets,Proc. London Math. Soc. 36 (1978), 369–384. · Zbl 0407.05006 · doi:10.1112/plms/s3-36.2.369
[3]	M. Deza, P. Erdos andN. M. Singhi, Combinatorial problems on subsets and their intersections,Advances in Mathematics, Suppl. Studies 1 (1978), 259–265.
[4]	M. Deza andI. G. Rosenberg, Cardinalités, de sommets et d’arêtes d’hypergraphes satisfaisant à certaines conditions d’intersection,Cahlers CERO. 20 (1978), 279–285.
[5]	P. Erdos, Problems and results in graph theory and combinatorial analysis,Proc. Fifth British Comb. Conf. 1975 Aberdeen, Congressus Numerantium,15 – Utilitas Mathematica, Winnipeg, 1976.
[6]	P. Erdos, Some remarks on the theory of graphs,Bull. Amer. Math. Soc. 53 (1947), 292–294. · Zbl 0032.19203 · doi:10.1090/S0002-9904-1947-08785-1
[7]	P. Erdos, Problems and results in chromatic graph theory, in:Proof techniques in graph theory (F. Harary ed.), Academic Press, London, 1969, 27–35.
[8]	P. Frankl, Extremal problems and coverings of the space,European J. Combs,1 (1980), 101–106. · Zbl 0463.05043
[9]	P. Frankl, A constructive lower bound for Ramsey numbers,Ars Comb. 3 (1977), 297–302. · Zbl 0397.05036
[10]	P. Frankl, Problem session,Proc. French–Canadian Joint Comb. Coll., Montreal 1978.
[11]	P. Frankl, Families of finite sets with prescribed cardinalities for pairwise intersections,Acta Math. Acad. Sci. Hung., to appear. · Zbl 0475.05064
[12]	P. Frankl andI. G. Rosenberg, An intersection problem for finite sets, Europ. J. Comb2 (1981). · Zbl 0461.05001
[13]	H. Hadwiger, Überdeckungssätze für den Euklidischen Raum,Portugaliae Math. 4 (1944), 140–144. · Zbl 0060.40610
[14]	H. Hadwiger, Überdeckung des Euklidischen Raumes durch kongruente Mengen,Portugaliae Math. 4 (1945), 238–242. · Zbl 0060.40611
[15]	D. G. Larman, A note on the realization of distances within sets in euclidean space,Comment. Math. Helvet. 53 (1978), 529–535. · Zbl 0408.52005 · doi:10.1007/BF02566096
[16]	D. G. Larman andC. A. Rogers, The realization of distances within sets in euclidean space,Mathematika 19 (1972), 1–24. · Zbl 0246.05020 · doi:10.1112/S0025579300004903
[17]	D. E. Raiskii, The realization of all distances in a decomposition ofR n inton + 1 parts (Russian)Mat. Zametki 7 (1970), 319–323.
[18]	D. K. Ray-Chaudhuri andR. M. Wilson, Ont-designs,Osaka J. Math. 12 (1975), 735–744. · Zbl 0342.05018
[19]	H. J. Ryser, An extension of a theorem of de Bruijn and Erdõs on combinatorial designs,J. Algebra 10 (1968), 246–261. · Zbl 0167.28001 · doi:10.1016/0021-8693(68)90099-9

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