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Show that, if the minimal number of edges that can be removed from an Eulerian graph G so that it stays Eulerian is k, G

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Show that, if the minimal number of edges that can be removed from an Eulerian graph G so that it stays Eulerian is k, G has a subgraph isomorphic to the cyclic graph Ck Show that, if the minimal number of edges that can be removed from an Eulerian graph G so that it stays Eulerian is k, G has a subgraph isomorphic to the cyclic graph Ck

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