Treewidth of grid subsets

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Abstract

Let Q n be the 3-dimensional n×n×n grid with all non-decreasing diagonals (including the facial ones) in its constituent unit cubes. Suppose that a set S ⊆ V (Q n ) separates the left side of the grid from the right side. We show that S induces a subgraph of tree-width at least \(\frac{n}{{\sqrt {18} }} = - 1\). We use a generalization of this claim to prove that the vertex set of Q n cannot be partitioned to two parts, each of them inducing a subgraph of bounded tree-width.

Mathematics Subject Classification (2000)

05C10 
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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.University of HaifaHaifaIsrael
  2. 2.Charles UniversityPragueCzech Republic
  3. 3.Department of Mathematics and StatisticsMcGill UniversityMontrealCanada

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