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Thilikos, Dimitris Chatzidimitriou, Ignasi Sau, Jean-Florent Raymond","submitted_at":"2015-10-14T01:41:15Z","abstract_excerpt":"Given two graphs $G$ and $H$, we define $\\textsf{v-cover}_{H}(G)$ (resp. $\\textsf{e-cover}_{H}(G)$) as the minimum number of vertices (resp. edges) whose removal from $G$ produces a graph without any minor isomorphic to ${H}$. Also $\\textsf{v-pack}_{H}(G)$ (resp. $\\textsf{v-pack}_{H}(G)$) is the maximum number of vertex- (resp. edge-) disjoint subgraphs of $G$ that contain a minor isomaorphic to $H$. We denote by $\\theta_r$ the graph with two vertices and $r$ parallel edges between them. 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