Reducing the domination number of P_3+kP_2-free graphs via one edge contraction

10/27/2020

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by   Esther Galby, et al.

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In this note, we consider the following problem: given a connected graph G, can we reduce the domination number of G by using only one edge contraction? We show that the problem is polynomial-time solvable on P_3+kP_2-free graphs for any k ≥ 0 which combined with results of [1,2] leads to a complexity dichotomy of the problem on H-free graphs.