Journal of Combinatorics

Volume 3 (2012)

Number 4

On balanced separators, treewidth, and cycle rank

Pages: 669 – 681



Hermann Gruber (Knowledgepark AG, München, Germany)


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 $k \cdot(1 + \log \frac{n}{k})$, 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.


vertex separator, treewidth, pathwidth, bandwidth, cycle rank, ordered coloring, vertex ranking, hypercube

2010 Mathematics Subject Classification

05C35, 05C40

Published 21 February 2013