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An edge of a k -connected graph is said to be k -contractible if its contraction results in a k -connected graph. A k -connected non-complete graph with no k -contractible edge, is called contraction critical k -connected. Let G be a contraction critical 5-connected graph, in this paper we show that G has at least \({\frac{1}{2}|G|}\) vertices of degree 5.
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