On the f -matching polytope and the fractional f -chromatic index.

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]