English

Revisiting Cases 2 and 11 of the Map Color Theorem

Combinatorics 2026-04-21 v2

Abstract

In 1968, Ringel and Youngs solved the remaining cases of the orientable Map Color Theorem by finding genus embeddings of the complete graphs KnK_n, for sufficiently large n2,8,11(mod12)n \equiv 2, 8, 11 \pmod{12}. Following the approach previously explored by the author for n8(mod12)n \equiv 8 \pmod{12}, we aim to streamline their constructions for n2,11(mod12)n \equiv 2, 11 \pmod{12} by finding families of current graphs with simpler patterns for the arc labelings.

Keywords

Cite

@article{arxiv.2509.06407,
  title  = {Revisiting Cases 2 and 11 of the Map Color Theorem},
  author = {Timothy Sun},
  journal= {arXiv preprint arXiv:2509.06407},
  year   = {2026}
}

Comments

10 pages, 10 figures