English

Hamilton decompositions of line graphs

Combinatorics 2020-12-03 v1

Abstract

It is proved that if a graph is regular of even degree and contains a Hamilton cycle, or regular of odd degree and contains a Hamiltonian 33-factor, then its line graph is Hamilton decomposable. This result partially extends Kotzig's result that a 33-regular graph is Hamiltonian if and only if its line graph is Hamilton decomposable, and proves the conjecture of Bermond that the line graph of a Hamilton decomposable graph is Hamilton decomposable.

Keywords

Cite

@article{arxiv.2012.00988,
  title  = {Hamilton decompositions of line graphs},
  author = {Darryn Bryant and Sara Herke and Barbara Maenhaut and Benjamin R. Smith},
  journal= {arXiv preprint arXiv:2012.00988},
  year   = {2020}
}

Comments

106 pages

R2 v1 2026-06-23T20:39:44.371Z