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Hadwiger’s Conjecture

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Abstract

This is a survey of Hadwiger’s conjecture from 1943, that for all t ≥ 0, every graph either can be t-coloured, or has a subgraph that can be contracted to the complete graph on t + 1 vertices. This is a tremendous strengthening of the four-colour theorem, and is probably the most famous open problem in graph theory.

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Acknowledgements

Thanks to several people who made suggestions for improvement, particularly Jacob Fox, Ken-ichi Kawarabayashi, Sasha Kostochka, Bojan Mohar, Sergey Norin, Sophie Spirkl, Robin Thomas, Bjarne Toft, Paul Wollan and David Wood. Supported by ONR grant N00014-10-1-0680 and NSF grant DMS-1265563.

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  1. Princeton University, Fine Hall, Washington Road, Princeton, NJ, 08544-1000, USA

    Paul Seymour

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  1. Paul Seymour
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Editors and Affiliations

  1. Department of Mathematics, Senior Research Mathematician, Princeton University, Princeton, New Jersey, USA

    John Forbes Nash, Jr.

  2. Department of Mathematics, Princeton University, Princeton, New Jersey, USA

    Michael Th. Rassias

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Seymour, P. (2016). Hadwiger’s Conjecture. In: Nash, Jr., J., Rassias, M. (eds) Open Problems in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-32162-2_13

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