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Given an undirected graph Formula: see text and a real edge-weight vector, the connected subgraph problem consists of finding a maximum-weight subset of edges which induces a connected subgraph of Formula: see text. In this paper, we establish a link between the complexity of the connected subgraph problem and the matching number. We study the separation problem associated with the so-called matching-partition inequalities, which were introduced by Didi Biha, Kerivin and Ng Polyhedral study of the connected subgraph problem, Discr. Math. 338 (2015) 80–92 for the connected subgraph polytope.
Biha et al. (Thu,) studied this question.