On Parameterized Path and Chordless Path Problems

Authors:
Yijia Chen;Jorg Flum
Affiliations:
Shanghai Jiaotong University, China;Universitat Freiburg, Germany
Venue:
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Year:
2007

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Abstract

We study the parameterized complexity of various path (and cycle) problems, the parameter being the length of the path. For example, we show that the problem of the existence of a maximal path of length k in a graph G is fixed-parameter tractable, while its counting version is #W[1]- complete. The corresponding problems for chordless (or induced) paths are W[2]-complete and #W[2]-complete respectively. With the tools developed in this paper we derive the NP-completeness of a related classical problem, thereby solving a problem due to Hedetniemi [17].