Abstract
We give a historical account of the parametrized results for the k-Path problem: given a graph G and a positive integer k, is there a simple path in G of length k. Throughout the years several ingenious approaches have been used, steadily decreasing the run time bound. Moreover, the techniques used have often found lots of other applications. We will revisit some of the old results, as well as cover the state-of-the-art techniques based on algebraic sieves. We will also briefly talk about what is known about counting k-paths.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Björklund, A. (2012). The Path Taken for k-Path. In: Thilikos, D.M., Woeginger, G.J. (eds) Parameterized and Exact Computation. IPEC 2012. Lecture Notes in Computer Science, vol 7535. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33293-7_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-33293-7_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33292-0
Online ISBN: 978-3-642-33293-7
eBook Packages: Computer ScienceComputer Science (R0)