מירב זהבי

A matching M in a graph G is an acyclic matching if the subgraph of G induced by the endpoints of the edges of M is a forest. Given a graph G and a positive integer l, Acyclic Matching asks whether G has an acyclic matching of size (i.e., the number of edges) at least l. In this paper, we first prove that assuming (Formula presented), there does not exist any FPT-approximation algorithm for Acyclic Matching that approximates it within a constant factor when parameterized by l. Our reduction is general in the sense that it also asserts FPT-inapproximability for Induced Matching and Uniquely Restricted Matching. We also consider three below-guarantee parameters for Acyclic Matching, viz. (Formula presented), where n is the number of vertices in G, MM(G) is the matching number of G, and IS(G) is the independence number of G. We note that the result concerning the below-guarantee parameter n/2-l is the most technical part of our paper. Also, we show that Acyclic Matching does not exhibit a polynomial kernel with respect to vertex cover number (or vertex deletion distance to clique) plus the size of the matching unless (Formula presented).