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Fast Exact Algorithms for Hamiltonicity in Claw-Free Graphs

Broersma, H. J.; Fomin, F. V.; Hof van 't, P.; Paulusma, D.

Authors

H. J. Broersma

F. V. Fomin

P. Hof van 't



Contributors

M. Habib
Editor

C. Paul
Editor

Abstract

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.

Citation

Broersma, H. J., Fomin, F. V., Hof van 't, P., & Paulusma, D. (2009). Fast Exact Algorithms for Hamiltonicity in Claw-Free Graphs. In M. Habib, & C. Paul (Eds.), Graph-theoretic concepts in computer science : 35th International Workshop, WG 2009, 24-26 June 2009, Montpellier, France ; revised papers (44-53). https://doi.org/10.1007/978-3-642-11409-0_4

Conference Name 35th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2009)
Conference Location Montpellier, France
Start Date Jun 24, 2009
End Date Jun 26, 2009
Publication Date Dec 1, 2009
Deposit Date Dec 15, 2009
Publisher Springer Verlag
Pages 44-53
Series Title Lecture notes in computer science
Series Number 5911
Book Title Graph-theoretic concepts in computer science : 35th International Workshop, WG 2009, 24-26 June 2009, Montpellier, France ; revised papers.
DOI https://doi.org/10.1007/978-3-642-11409-0_4
Public URL https://durham-repository.worktribe.com/output/1159535
Publisher URL http://www.springerlink.com/content/c887p41650ut987l/


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