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.
| Original language | English |
|---|---|
| Article number | 113208 |
| Journal | Discrete Mathematics |
| Volume | 346 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 2023 |
Keywords
- Connectivity
- Extremal graph
- Hamiltonian graph
- Size
- Traceable graph