On 13-Crossing-Critical Graphs with Arbitrarily Large Degrees
| Autoři | |
|---|---|
| Rok publikování | 2021 |
| Druh | Článek ve sborníku |
| Konference | Extended Abstracts EuroComb 2021. Trends in Mathematics |
| Fakulta / Pracoviště MU | |
| Citace | |
| www | http://arxiv.org/abs/2105.01104 |
| Doi | http://dx.doi.org/10.1007/978-3-030-83823-2_9 |
| Klíčová slova | Graph; Crossing number; Crossing-critical families |
| Popis | A surprising result of Bokal et al. proved that the exact minimum value of c such that c-crossing-critical graphs do not have bounded maximum degree is c=13. The key to the result is an inductive construction of a family of 13-crossing-critical graphs with many vertices of arbitrarily high degrees. While the inductive part of the construction is rather easy, it all relies on the fact that a certain 17-vertex base graph has the crossing number 13, which was originally verified only by a machine-readable computer proof. We now provide a relatively short self-contained computer-free proof. |
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