What is hypohamiltonian?

Some articles on hypohamiltonian:

Hypohamiltonian Graph - Enumeration
... in 1973 that for all sufficiently large n there exists a hypohamiltonian graph with n vertices ... A complete list of hypohamiltonian graphs with at most 17 vertices is known they are the 10-vertex Petersen graph, a 13-vertex graph and a 15-vertex graph ... There exist at least thirteen 18-vertex hypohamiltonian graphs ...
Hypohamiltonian Graph - Properties
... Every hypohamiltonian graph must be 3-vertex-connected, as the removal of any two vertices leaves a Hamiltonian path, which is connected ... There exist n-vertex hypohamiltonian graphs in which the maximum degree is n/2, and in which there are approximately n2/4 edges ... For some time it was unknown whether a hypohamiltonian graph could be planar, but several examples are now known, the smallest of which has 40 vertices ...
Hypohamiltonian Graph - Applications
... Hypohamiltonian graphs arise in integer programming solutions to the traveling salesman problem certain kinds of hypohamiltonian graphs define facets of the traveling salesman polytope, a shape ... computational complexity of determining whether a graph is hypohamiltonian, although unknown, is likely to be high, making it difficult to find facets of these types except for those defined ...