On Balanced Separators, Treewidth, and Cycle Rank
Discrete Mathematics
2015-03-17 v2 Combinatorics
Abstract
We investigate relations between different width parameters of graphs, in particular balanced separator number, treewidth, and cycle rank. Our main result states that a graph with balanced separator number k has treewidth at least k but cycle rank at most k(1 + log (n/k)), thus refining the previously known bounds, as stated by Robertson and Seymour (1986) and by Bodlaender et al. (1995). Furthermore, we show that the improved bounds are best possible.
Cite
@article{arxiv.1012.1344,
title = {On Balanced Separators, Treewidth, and Cycle Rank},
author = {Hermann Gruber},
journal= {arXiv preprint arXiv:1012.1344},
year = {2015}
}
Comments
Version 2: revised version, 8 pages