Let Qn 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 (Qn) separates the left side of the grid from the right side. We show that S induces a subgraph of tree-width at least (Formula presented.). We use a generalization of this claim to prove that the vertex set of Qn cannot be partitioned to two parts, each of them inducing a subgraph of bounded tree-width.
Bibliographical notePublisher Copyright:
© 2017 János Bolyai Mathematical Society and Springer-Verlag GmbH Germany
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Computational Mathematics