PreprintCC BY 4.0arXiv
Small covers and the Four Color Theorem
Abstract
We give a combinatorial proof that every simple convex $3$-polytope admits a small cover without using the Four Color Theorem. We also prove that the assertion that every simple plane triangulation admits a mod~$2$ characteristic function with at most five values is equivalent to the Four Color Theorem.
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BibTeX
@misc{choi2026small,
title = {{Small covers and the Four Color Theorem}},
author = {Suyoung Choi and Ringi Kim},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29131},
eprint = {2610.29131},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29131},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Small covers and the Four Color Theorem
AU - Suyoung Choi
AU - Ringi Kim
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29131
UR - https://arxiv.org/abs/2610.29131
AB - We give a combinatorial proof that every simple convex $3$-polytope admits a small cover without using the Four Color Theorem. We also prove that the assertion that every simple plane triangulation admits a mod~$2$ characteristic function with at most five values is equivalent to the Four Color Theorem.
ER -