English

On Genus g Orientable Crossing Numbers of Small Complete Graphs

Combinatorics 2019-02-08 v1

Abstract

The current state of knowledge of genus g orientable crossing numbers of complete graphs through K11 is reviewed. It is shown that cr3(K10)=3, cr3(K11)<=14, and cr4(K11)=4. It is established with the aid of an algorithm that there are precisely two non-isomorphic embeddings of K9 with a hexagon with all its vertices distinct on a surface of genus 3.

Keywords

Cite

@article{arxiv.1902.02759,
  title  = {On Genus g Orientable Crossing Numbers of Small Complete Graphs},
  author = {Yoonah Lee},
  journal= {arXiv preprint arXiv:1902.02759},
  year   = {2019}
}

Comments

20 pages, 7 figures