The maximum size of a nonhamiltonian graph with given order and connectivity

摘要

Motivated by work of Erdos, 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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