A note on planar graphs with large width parameters and small grid-minors

A. Grigoriev, B. Marchal, N. Usotskaya, I. Todinca

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Abstract

Given a graph gg with tree-width ?(g)?(g), branch-width ß(g)ß(g), and side size of the largest square grid-minor ?(g)?(g), it is known that ?(g)=ß(g)=?(g)+1=32ß(g)?(g)=ß(g)=?(g)+1=32ß(g). In this paper, we introduce another approach to bound the side size of the largest square grid-minor specifically for planar graphs. The approach is based on measuring the distances between the faces in an embedding of a planar graph. We analyze the tightness of all derived bounds. In particular, we present a class of planar graphs where ?(g)=ß(g)?(g)=ß(g)?(g)=?32?(g)?-1.
Original languageEnglish
Pages (from-to)1262-1269
Number of pages8
JournalDiscrete Applied Mathematics
Volume160
Issue number7-8
DOIs
Publication statusPublished - 1 Jan 2012

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