Abstract
A method is presented for evaluating the bidimension of a finite binary relation, i.e., the number of biorders (Guttman relations) needed to yield the relation as their intersection. In case the relation is induced by a binary data matrix, the bidimension equals the minimal number of dimensions needed for a representation of the data matrix according to the conjunctive model of C. H. Coombs and R. C. Kao ( Nonmetric factor analysis, Engineering Research Bulletin No. 38, Univ. of Michigan Press, Ann Arbor, 1955) . Central to the evaluation of the bidimension is its characterization, provided by J.-P. Doignon, A. Ducamp, and J.-C. Falmagne ( Journal of Mathematical Psychology, 28, 73–109, 1984) , as the chromatic number of some associated hypergraph. A procedure is described to reduce hypergraphs of this kind to subhypergraphs with the same chromatic number. This reduction can be used throughout in applying a recurrence relation that expresses the chromatic number of a hypergraph in terms of the chromatic numbers of some of its subhypergraphs.
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