The property of the graph is the following: For any vertex, there is a hamiltonian path starting with this vertex, but the graph is not hamiltonian. The following graph is a small example:
Important examples are hypohamiltonian graphs (deleting each vertex leads to a hamiltonian graph, but the graph is not hamiltonian ; for example the Petersen graph)
- Is there a name for such graphs?
- Which numbers of vertices are possible for such a graph?
- Is there a knight graph with this property? (See mathworld knight graph for more details. I think the answer is no.)