Problems in Topological Graph Theory


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Dan Archdeacon passed away in February 2015. This site contains his compiled problems in topological graph theory as he left it. It has not been updated recently. However we hope that it can still be of use to researchers in the field.


Compiled by Dan Archdeacon

List Started: August 1995
Converted to the web: September 1998
Extensive revisions: December 2003


Abstract

Do you think you've got problems? I know I do. This paper contains an ongoing list of open questions in topological graph theory. If you are interested in adding a problem to this list please contact me at the addresses above. The spirit is inclusive---don't submit a problem you're saving for your graduate student. If it appears here, it's fair game. If you solve one of the problems, know some additional history, recognize it as phrased incorrectly, or think itís just a stupid question, please let me know so that I can keep the list up-to-date. I've taken quite a bit of liberty editing the submissions. I apologize for any errors introduced. My original goal was to update the list monthly, however, that has proven too difficult. There is no guarantee that references are up-to-date.

Enjoy my problems---I do!


Table of Contents

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The Problems

Classical questions on genus

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Obstruction to embeddings

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Paths, cycles, and matchings

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Coloring graphs and maps

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 List colorings and choosability

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Flows

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Locally planar embeddings

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Crossing numbers

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Drawings

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Representating graphs and embeddings

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Geometric graphs

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Symmetries

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Random topological graph theory

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Book embeddings

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Other problems on planar graphs

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Miscellaneous problems

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Solved problems from previous editions

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Under construction (material on these pages may not be up-to-date)

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The End