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,Parameterized Results on Acyclic Matchings with Implications for Related Problems,., . asks whether . has an acyclic matching of . (i.e., the number of edges) at least .. In this paper, we first prove that assuming ., there does not exist any .-approximation algorithm for . that approximates it within a constant factor when parameterized by .. Our reduction is general in the sens

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,Degreewidth: A New Parameter for Solving Problems on Tournaments,lic. The degreewidth of a tournament . denoted by . is the minimum value . for which we can find an ordering . of the vertices of . such that every vertex is incident to at most . backward arcs (. an arc . such that .). Thus, a tournament is acyclic if and only if its degreewidth is zero. Additional