• Corpus ID: 235294273

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

  title={The maximum size of a nonhamiltonian graph with given order and connectivity},
  author={Xingzhi Zhan and Leilei Zhang},
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… 


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