On the parameterized complexity of the acyclic matching problem

A matching is a set of edges in graph with no common endpoint. M called acyclic if the induced subgraph on endpoints acyclic. Given G and an integer k, Acyclic Matching problem seeks for size k G. The known to be NP-complete. In this paper, we investigate complexity different aspects. First, prove that remains NP-complete class planar bipartite graphs maximum degree three arbitrarily large girth. Also, line four. Moreover, study parameterized problem. particular, W[1]-hard respect parameter k. On other hand, fixed tractable parameters treewidth, modular-width (k,c4), where c4 number cycles length 4 input graph. We also every proper minor-closed (including graphs).