Parameterized Edge Hamiltonicity
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. 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. 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-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.
Cite
@article{arxiv.1403.2041,
title = {Parameterized Edge Hamiltonicity},
author = {Michael Lampis and Kazuhisa Makino and Valia Mitsou and Yushi Uno},
journal= {arXiv preprint arXiv:1403.2041},
year = {2014}
}