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Problems and results in combinatorial analysis. (English) Zbl 0361.05037
Colloq. int. Teorie comb., Roma 1973, Tomo II, 3-17 (1976).
[For the entire collection see Zbl 0348.00004.]
This paper and the paper considered in the next review are continuations of a series of expository papers by the author in which he surveys a number of combinatorial problems on which he and his collaborators have worked. The first four sections of this paper deal with extremal problems on graphs and hypergraphs, and the fith section is devoted to problems on subsets of a set; several of these problems involve constructions related to block designs. The last section, containing some miscellaneous problems, concludes with the following conjecture. Let \(A_1,\dots,A_n\) denote n sets of size \(n\) any two of which have at most one element in common. Is it possible to colour the elements of \(\cup A_1\) with n colours so that each set \(A_1\) contains an element of each colour?

MSC:
05C35 Extremal problems in graph theory
05A05 Permutations, words, matrices
05C15 Coloring of graphs and hypergraphs
00A07 Problem books