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Critical sets for latin squares, graphs and block designs: A survey. (English) Zbl 0955.05019
From the introduction: The idea of a critical set was first proposed with reference to latin squares by J. Nelder (1977) who has told the present author that, contrary to earlier supposition, he had no particular application in mind. Later, the same idea arose in connection with block designs and much more recently with reference to graph colourings. Meanwhile, applications to various coding problems have been proposed (for example in [J. Cooper, D. Donovan and J. Seberry, Bull. Inst. Comb. Appl. 12, 33-43 (1994; Zbl 0835.05009)]).
In this survey, we shall follow the historical order, first discussing latin squares, then block designs (briefly) and finally graphs.

05B15 Orthogonal arrays, Latin squares, Room squares
05B05 Combinatorial aspects of block designs
05C15 Coloring of graphs and hypergraphs
05C35 Extremal problems in graph theory