Finding Hamiltonian circuits in quasi-adjoint graphs

Authors:
Jacek Blazewicz;Marta Kasprzak;Benjamin Leroy-Beaulieu;Dominique de Werra
Affiliations:
Institute of Computing Science, Poznan University of Technology, Poznan, Poland and Institute of Bioorganic Chemistry, Polish Academy of Sciences, Poznan, Poland;Institute of Computing Science, Poznan University of Technology, Poznan, Poland and Institute of Bioorganic Chemistry, Polish Academy of Sciences, Poznan, Poland;IMA-ROSE, Ecole Polytechnique Fédérale de Lausanne, Switzerland;IMA-ROSE, Ecole Polytechnique Fédérale de Lausanne, Switzerland
Venue:
Discrete Applied Mathematics
Year:
2008

Citing 6
Cited 2

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Abstract

This paper is motivated by a method used for DNA sequencing by hybridization presented in [Jacek Blazewicz, Marta Kasprzak, Computational complexity of isothermic DNA sequencing by hybridization, Discrete Appl. Math. 154 (5) (2006) 718-729]. This paper presents a class of digraphs: the quasi-adjoint graphs. This class includes the ones used in the paper cited above. A polynomial recognition algorithm in O(n^3), as well as a polynomial algorithm in O(n^2+m^2) for finding a Hamiltonian circuit in these graphs are given. Furthermore, some results about related problems such as finding a Eulerian circuit while respecting some forbidden transitions (a path with three vertices) are discussed.