Let G be a k-connected graph of order n with |E(G)| > (n−k 2) + k 2. Then for (k = 1, n 3), (k = 2, n 10), and (k = 3, n 16), G is hamiltonian. The bounds are tight and for k = 1, (k = 2, n 12), and (k = 3, n 18) the extremal graphs are unique. A general bound will also be given for the number of edges in a nonhamiltonian k-connected graph, but the bound is… (More)
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