Regular Article
Domino Treewidth

https://doi.org/10.1006/jagm.1996.0854Get rights and content

Abstract

We consider a special variant of tree-decompositions, calleddomino tree-decompositions, and the related notion ofdomino treewidth. In a domino tree-decomposition, each vertex of the graph belongs to at most two nodes of the tree. We prove that for everyk, d, there exists a constantck, dsuch that a graph with treewidth at mostkand maximum degree at mostdhas domino treewidth at mostck, d. The domino treewidth of a tree can be computed inO(n2 log n) time. There exist polynomial time algorithms that—for fixedk—decide whether a given graphGhas domino treewidth at mostk. Ifkis not fixed, this problem is NP-complete. The domino treewidth problem is hard for the complexity classesW[t] for allt  N, and hence the problem for fixedkis unlikely to be solvable inO(nc) time, wherecis a constant, not depending onk.

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This author was partially supported by the ESPRIT Basic Research Actions of the European Community under Contract 7141 (Project ALCOM II).

This author was supported by the ESPRIT Basic Research Working Group COMPUGRAPH II.

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