The Gn, m Phase Transition is Not Hard for the Hamiltonian Cycle Problem

Using an improved backtrack algorithm with sophisticated pruning techniques, we revise previous observations correlating a high frequency of hard to solve Hamiltonian cycle instances with the Gn;m phase transition between Hamiltonicity and non-Hamiltonicity. Instead all tested graphs of 100 to 1500 vertices are easily solved. When we arti cially restrict the degree sequence with a bounded maximum degree, although there is some increase in di culty, the frequency of hard graphs is still low. When we consider more regular graphs based on a generalization of knight's tours, we observe frequent instances of really hard graphs, but on these the average degree is bounded by a constant. We design a set of graphs with a feature our algorithm is unable to detect and so are very hard for our algorithm, but in these we can vary the average degree from O1 to On. We have so far found no class of graphs correlated with the Gn;m phase transition which asymptotically produces a high frequenc...

• Type: Journal
• Year: 1998
• Where: JAIR
• Authors: Basil Vandegriend, Joseph C. Culberson
• Keywords: Hamiltonian Cycle Instances, Hard Graphs, JAIR 1998, Sophisticated Pruning Techniques