Geodesic
A note on domino treewidth
Discrete mathematics & theoretical computer science, Tome 3 (1998-1999) no. 4.

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In [DO95], Ding and Oporowski proved that for every k, and d, there exists a constant c_k,d, such that every graph with treewidth at most k and maximum degree at most d has domino treewidth at most c_k,d. This note gives a new simple proof of this fact, with a better bound for c_k,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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     author = {Bodlaender, Hans L.},
     title = {A note on domino treewidth},
     journal = {Discrete mathematics & theoretical computer science},
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Bodlaender, Hans L. A note on domino treewidth. Discrete mathematics & theoretical computer science, Tome 3 (1998-1999) no. 4. doi : 10.46298/dmtcs.256. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.256/

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