### Abstract

Given a simple planar graph with tree-width w and side size of the largest square grid minor g, it is known that g?w?5g-1g?w?5g-1. Thus, the side size of the largest grid minor is a constant approximation for the tree-width in planar graphs. In this work we analyze the lower bounds of this approximation. In particular, we present a class of planar graphs with ?3g/2?-1?w?3g/2??3g/2?-1?w??3g/2?. We conjecture that in the worst case w=2g+o(g)w=2g+o(g). For this conjecture we have two candidate classes of planar graphs.

Original language | English |
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Pages (from-to) | 35-42 |

Number of pages | 8 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 32 |

DOIs | |

Publication status | Published - 1 Jan 2009 |

## Cite this

Grigoriev, A., Marchal, L., & Usotskaya, N. (2009). On planar graphs with large tree-width and small grid minors.

*Electronic Notes in Discrete Mathematics*,*32*, 35-42. https://doi.org/10.1016/j.endm.2009.02.006