Abstract
The critical problem of matroid theory can be posed in the more general context of finite relations. Given a relation R between the finite sets S and T, the critical problem is to determine the smallest number n such that there exists an n-tuple ( u 1,…, u n ) of elements from T such that for every x in S, there exists a u 1 such that xRu i . All the enumerative results, in particular, the Tutte decomposition and Möbius function formula, can be rephrased so that they still hold. In this way, we obtain a uniform approach to all the classical critical problems.
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