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Journal Articles Discrete Applied Mathematics Year : 2017

Minimum Size Tree-Decompositions


We study in this paper the problem of computing a tree-decomposition of a graph with width at most k and minimum number of bags. More precisely, we focus on the following problem: given a fixed $k ≥ 1$, what is the complexity of computing a tree-decomposition of width at most k with minimum number of bags in the class of graphs with treewidth at most k? We prove that the problem is NP-complete for any fixed $k ≥ $4 and polynomial for $k ≤ 2$; for $k = 3$, we show that it is polynomial in the class of trees and 2-connected outerplanar graphs.
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hal-01620389 , version 1 (23-11-2017)



Bi Li, Fatima Zahra Moataz, Nicolas Nisse, Karol Suchan. Minimum Size Tree-Decompositions. Discrete Applied Mathematics, 2017, ⟨10.1016/j.dam.2017.01.030⟩. ⟨hal-01620389⟩
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