Abstract

Motivated by work of Erdős, Ota determined the maximum size g(n,k) of a k-connected nonhamiltonian graph of order n in 1995. But for some pairs n,k, the maximum size is not attained by a graph of connectivity k. For example, g(15,3)=77 is attained by a unique graph of connectivity 7, not 3. In this paper we obtain more precise information by determining the maximum size of a nonhamiltonian graph of order n and connectivity k, and determining the extremal graphs. Consequently we solve the corresponding problem for nontraceable graphs.

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