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 -factor, then its line graph is Hamilton decomposable. This result partially extends Kotzig's result that a -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.
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