Treewidth of grid subsets

Eli Berger; Zdenĕk Dvořák; Sergey Norin

doi:10.1007/s00493-017-3548-5

Treewidth of grid subsets

Eli Berger, Zdenĕk Dvořák, Sergey Norin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 (Formula presented.). 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.

Original language	English
Pages (from-to)	1-16
Number of pages	16
Journal	Combinatorica
DOIs	https://doi.org/10.1007/s00493-017-3548-5
State	Published - 14 Aug 2017

Bibliographical note

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

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Computational Mathematics

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10.1007/s00493-017-3548-5

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abstract = "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.",

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Treewidth of grid subsets

Abstract

Bibliographical note

ASJC Scopus subject areas

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