English

Splitting cubic circle graphs

Combinatorics 2016-07-13 v1

Abstract

We show that every 3-regular circle graph has at least two pairs of twin vertices; consequently no such graph is prime with respect to the split decomposition. We also deduce that up to isomorphism, K_4 and K_{3,3} are the only 3-connected, 3-regular circle graphs.

Keywords

Cite

@article{arxiv.1504.01143,
  title  = {Splitting cubic circle graphs},
  author = {Lorenzo Traldi},
  journal= {arXiv preprint arXiv:1504.01143},
  year   = {2016}
}

Comments

18 pages, 15 figures

R2 v1 2026-06-22T09:10:23.112Z