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 ...
... 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 ...
... 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 ...
... 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 ...
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