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

Abstract

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 polynomialtime solvable on P3 + kP2-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.