### A note on domino treewidth

*Hans L. Bodlaender*

#### Abstract

In [DO95], Ding and Oporowski proved that for every k, and d, there exists a constant ck,d, such that every graph with treewidth at most k and maximum degree at most d has domino treewidth at most ck,d. This note gives a new simple proof of this fact, with a better bound for ck,d, namely (9k+7)d(d+1) -1. It is also shown that a lower bound of Ω(kd) holds: there are graphs with domino treewidth at least 1/12 × kd-1, treewidth at most k, and maximum degree at most d, for many values k and d. The domino treewidth of a tree is at most its maximum degree.

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