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Graphic matroid
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==Matroid connectivity== A matroid is said to be connected if it is not the direct sum of two smaller matroids; that is, it is connected if and only if there do not exist two disjoint subsets of elements such that the rank function of the matroid equals the sum of the ranks in these separate subsets. Graphic matroids are connected if and only if the underlying graph is both [[connected graph|connected]] and [[k-vertex-connected graph|2-vertex-connected]].<ref name="tutte65"/>
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