In this paper, we study the following problem: given a connected graph $ G $, can we reduce
the domination number of $ G $ by at least one using $ k $ edge contractions, for some fixed
integer $ k\geq 0$? We present positive and negative results regarding the computational
complexity of this problem.

In this work, we study the following problem: given a connected graph G, can we reduce the
domination number of G by at least one using k edge contractions, for some fixed integer k>
0? We show that for k= 1 (resp. k= 2), the problem is NP-hard (resp. coNP-hard). We further
prove that for k= 1, the problem is W [1]-hard parameterized by domination number plus the
mim-width of the input graph, and that it remains NP-hard when restricted to chordal {P 6, P
4+ P 2}-free graphs, bipartite graphs and {C 3,…, C ℓ}-free graphs for any ℓ≥ 3. We also�…