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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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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