Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10151229 | Discrete Applied Mathematics | 2018 | 11 Pages |
Abstract
We study the parameterized complexity of the classical Edge Hamiltonian Path  problem and give several fixed-parameter tractability results. First, we settle an open question of Demaine et al. (2014) by showing that Edge Hamiltonian Path  is FPT parameterized by vertex cover, and that it also admits a cubic kernel. We then show fixed-parameter tractability even for a generalization of the problem to arbitrary hypergraphs, parameterized by the size of a (supplied) hitting set. As an interesting consequence, we show that this implies an FPT algorithm for (Vertex) Hamiltonian Path parameterized by (vertex) clique cover. We also consider the problem parameterized by treewidth or clique-width. Surprisingly, we show that the problem is FPT for both of these standard parameters, in contrast to its vertex version, which is W[1]-hard for clique-width. Our technique, which may be of independent interest, relies on a structural characterization of clique-width in terms of treewidth and complete bipartite subgraphs due to Gurski and Wanke.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Michael Lampis, Kazuhisa Makino, Valia Mitsou, Yushi Uno,