2-edge connected subgraph problem, complete description

Abstract

Our work focus on node weighted 2-edge connected subgraph problem defined by Baiou [?]. Given a graph G = (V, E), a node r ∈ V and cost (weight) function on nodes and edges, the r-2-edge connected subgraph problem consists on finding a 2-edge connected subgraph in G containing r whose total cost (weight) on both nodes and edges is minimized. We study a class of graphs for which the polytope associated to the r-2-edge connected subgraph problem is completely described by the trivial inequalities and the inequalities so called generalized cut inequalities. After that, we investigate a class of valid inequalities given by Baiou and Correa in the case of cordless multi-cycle graphs.