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The Excluded Tree Minor Theorem Revisited

Published online by Cambridge University Press:  27 September 2023

Vida Dujmović ,
Robert Hickingbotham ,
Gwenaël Joret ,
Piotr Micek ,
Pat Morin  and
David R. Wood Open the ORCID record for David R. Wood [Opens in a new window]
Vida Dujmović
Affiliation:
School of Computer Science and Electrical Engineering, University of Ottawa, Ottawa, ON, Canada
Robert Hickingbotham
Affiliation:
School of Mathematics, Monash University, Melbourne, VIC, Australia
Gwenaël Joret
Affiliation:
Département d’Informatique, Université libre de Bruxelles, Bruxelles, Belgium
Piotr Micek*
Affiliation:
Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland
Pat Morin
Affiliation:
School of Computer Science, Carleton University, Ottawa, ON, Canada
David R. Wood
Affiliation:
School of Mathematics, Monash University, Melbourne, VIC, Australia
*
Corresponding author: Piotr Micek; Email: piotr.micek@uj.edu.pl
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Abstract

We prove that for every tree $T$ of radius $h$, there is an integer $c$ such that every $T$-minor-free graph is contained in $H\boxtimes K_c$ for some graph $H$ with pathwidth at most $2h-1$. This is a qualitative strengthening of the Excluded Tree Minor Theorem of Robertson and Seymour (GM I). We show that radius is the right parameter to consider in this setting, and $2h-1$ is the best possible bound.

Keywords

Structural graph theorypathwidthgraph minors
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 33 , Issue 1 , January 2024 , pp. 85 - 90
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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Footnotes

†

Vida Dujmović: Research supported by NSERC, and a Gordon Preston Fellowship from the School of Mathematics at Monash University.

‡

Robert Hickingbotham: Research supported by Australian Government Research Training Program Scholarships.

§

Gwenaël Joret: Supported by the Australian Research Council, and by a CDR grant and a PDR from the National Fund for Scientific Research (FNRS).

Pat Morin: Research supported by NSERC.

∥

David R. Wood: Research supported by the Australian Research Council.

References

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