# A Note on Exact Algorithms for Vertex Ordering Problems on Graphs

@article{Bodlaender2011ANO,
title={A Note on Exact Algorithms for Vertex Ordering Problems on Graphs},
author={Hans L. Bodlaender and F. Fomin and Arie M. C. A. Koster and Dieter Kratsch and Dimitrios M. Thilikos},
journal={Theory of Computing Systems},
year={2011},
volume={50},
pages={420-432}
}
• Published 1 April 2012
• Mathematics, Computer Science
• Theory of Computing Systems
In this note, we give a proof that several vertex ordering problems can be solved in O∗(2n) time and O∗(2n) space, or in O∗(4n) time and polynomial space. The algorithms generalize algorithms for the Travelling Salesman Problem by Held and Karp (J. Soc. Ind. Appl. Math. 10:196–210, 1962) and Gurevich and Shelah (SIAM J. Comput. 16:486–502, 1987). We survey a number of vertex ordering problems to which the results apply.
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