Abstract
We consider a special variant of tree-decompositions, called domino tree-decompositions, and the related notion of domino treewidth. In a domino tree-decomposition, each vertex of the graph belongs to at most two nodes of the tree. We prove that for every k, d, there exists a constant C k,d such that a graph with treewidth at most k and maximum degree at most d has domino treewidth at most C k,d The domino treewidth of a tree can be computed in O(n 2 log n) time. There exist polynomial time algorithms that — for fixed k — decide whether a given graph G has domino treewidth at most k. If k is not fixed, this problem is NP-complete. The domino treewidth problem is hard for the complexity classes W[t] for all t ξ N, and hence the problem for fixed k is unlikely to be solvable in O(n c), where c is a constant, not depending on k.
This author was partially supported by the ESPRIT Basic Research Actions of the EC under contract 7141 (project ALCOM II).
This author was supported by the ESPRIT Basic Research Working Group COMPUGRAPH II.
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Bodlaender, H.L., Engelfriet, J. (1995). Domino treewidth. In: Mayr, E.W., Schmidt, G., Tinhofer, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 1994. Lecture Notes in Computer Science, vol 903. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59071-4_33
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DOI: https://doi.org/10.1007/3-540-59071-4_33
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