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A celebrated theorem of Pippenger states that any almost regular hypergraph with small codegrees has an almost perfect matching. We show that one can find such an almost perfect matching which is 'pseudorandom', meaning that, for instance, the matching contains as many edges from a given set of edges as predicted by a heuristic argument. [ABSTRACT FROM AUTHOR]

Our motivation is the question how similar thef-colouring problem is to the classic edge-colouring problem, particularly with regard to graph parameters. In 2010, Zhanget al.[On the fractional f-chromatic index of a graph, Int. J. Comput. Math. 87 (2010), pp. 3359–3369] gave a new description of thef-matching polytope and thereby derived a formula for the fractionalf-chromatic index stating that the fractionalf-chromatic index is equal to the maximum of the fractional maximumf-degree and the fractionalf-density. Unfortunately, this formula is incorrect. We present counterexamples for both the description of thef-matching polytope and the formula for the fractionalf-chromatic index. Finally, we prove a short lemma concerning the generalization of Goldberg's conjecture. [ABSTRACT FROM PUBLISHER]