Fast Exact Algorithms for Hamiltonicity in Claw-Free Graphs

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

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, June). Fast Exact Algorithms for Hamiltonicity in Claw-Free Graphs. Presented at 35th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2009), Montpellier, France

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 35th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2009)
• Start Date: Jun 24, 2009
• End Date: Jun 26, 2009
• Publication Date: Dec 1, 2009
• Deposit Date: Dec 15, 2009
• Print ISSN: 0302-9743
• 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/