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Fast exact algorithms for hamiltonicity in claw-free graphs.

Broersma, H. J. and Fomin, F. V. and Hof van 't, P. and Paulusma, Daniel (2009) 'Fast exact algorithms for hamiltonicity in claw-free graphs.', in Graph-theoretic concepts in computer science : 35th International Workshop, WG 2009, 24-26 June 2009, Montpellier, France ; revised papers. Berlin: Springer, pp. 44-53. Lecture notes in computer science. (5911).


The Hamiltonian Cycle problem asks if an n-vertex graph G has a cycle passing through all vertices of G. This problem is a classic NP-complete problem. So far, finding an exact algorithm that solves it in O *(α n ) time for some constant α< 2 is a notorious open problem. For a claw-free graph G, finding a hamiltonian cycle is equivalent to finding a closed trail (eulerian subgraph) that dominates the edges of some associated graph H. Using this translation we obtain two exact algorithms that solve the Hamiltonian Cycle problem for the class of claw-free graphs: one algorithm that uses O *(1.6818 n ) time and exponential space, and one algorithm that uses O *(1.8878 n ) time and polynomial space.

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Date of first online publication:2009
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