A constructive characterization of contraction critical 8-connected graphs with minimum degree 9

Abstract 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 graph without k -contractible edge is said to be contraction critically k -connected. Y. Egawa and W. Mader, independently, showed that the minimum degree of a contraction critical k -connected graph is at most 5 k 4 − 1 . Hence, the minimum degree of a contraction critical 8-connected graph is either 8 or 9. This paper shows that a graph G is a contraction critical 8-connected graph with minimum degree 9 if and only if G is the strong product of a contraction critical 4-connected graph H and K 2 .

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