Towards Characterization of 5-List-Colorability of Toroidal Graphs
<|reference_start|>Towards Characterization of 5-List-Colorability of Toroidal Graphs: Through computer-assisted enumeration, we list minimal obstructions for 5-choosability of graphs on the torus with the following additional property: There exists a cyclic system of non-contractible triangles around the torus where the consecutive triangles are at distance at most four. This condition is satisfied by all previously known obstructions, and we verify that there are no additional obstructions with this property. This supports the conjecture that a toroidal graph is 5-choosable if and only if it is 5-colorable.<|reference_end|>
@article{dvořák2024towards,
    title={Towards Characterization of 5-List-Colorability of Toroidal Graphs},
    author={Zdenv{e}k Dvov{r}'ak, F'elix Moreno Pe~narrubia},
    journal={arXiv preprint arXiv:2407.18800},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.18800},
    primaryClass={math.CO cs.DM}
}