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Given two graphs G and H, we define $$\mathsf{v}\hbox {-}\mathsf{cover}_{H}(G)$$ v-coverH(G) (resp. $$\mathsf{e}\hbox {-}\mathsf{cover}_{H}(G)$$ e-coverH(G) ) as the minimum number of vertices (resp. edges) whose removal from G produces a graph without any minor isomorphic to H. Also $$\mathsf{v}\hbox {-}\mathsf{pack}_{H}(G)$$ v-packH(G) (resp. $$\mathsf{e}\hbox {-}\mathsf{pack}_{H}(G)$$ e-packH(G)...
For every r∈N, we denote by θr the multigraph with two vertices and r parallel edges. Given a graph G, we say that a subgraph H of G is a model of θr in G if H contains θr as a contraction. We prove that the following edge variant of the Erdős–Pósa property holds for every r⩾2: if G is a graph and k is a positive integer, then either G contains a packing of k mutually edge-disjoint models of θr,...
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