Treewidth of Cartesian Products of Highly Connected Graphs

Details Treewidth of Cartesian Products of Highly Connected Graphs Treewidth of Cartesian Products of Highly Connected Graphs

2011-05-09

arxiv.org/abs/1105.1586v2

Mathematics

Combinatorics

Scientific paper

The following theorem is proved: For all $k$-connected graphs $G$ and $H$
each with at least $n$ vertices, the treewidth of the cartesian product of $G$
and $H$ is at least $k(n -2k+2)-1$. For $n\gg k$ this lower bound is
asymptotically tight for particular graphs $G$ and $H$. This theorem
generalises a well known result about the treewidth of planar grid graphs.

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