A $1$-factorisation of a graph $G$ is a decomposition of $G$ into edge-disjoint $1$-factors (perfect matchings), and a perfect $1$-factorisation is a $1$-factorisation in which the union of any two of the $1$-factors is a Hamilton cycle. We consider the problem of the existence of perfect $1$-factorisations of even order circulant graphs with small degree. In particular, we characterise the $3$-regular circulant graphs that admit a perfect $1$-factorisation and we solve the existence problem for a large family of $4$-regular circulants. Results of computer searches for perfect $1$-factorisations of $4$-regular circulant graphs of orders up to $30$ are provided and some problems are posed.
@article{10_37236_2264,
author = {Sarada Herke and Barbara Maenhaut},
title = {Perfect 1-factorisations of circulants with small degree},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {1},
doi = {10.37236/2264},
zbl = {1266.05119},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2264/}
}
TY - JOUR
AU - Sarada Herke
AU - Barbara Maenhaut
TI - Perfect 1-factorisations of circulants with small degree
JO - The electronic journal of combinatorics
PY - 2013
VL - 20
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/2264/
DO - 10.37236/2264
ID - 10_37236_2264
ER -
%0 Journal Article
%A Sarada Herke
%A Barbara Maenhaut
%T Perfect 1-factorisations of circulants with small degree
%J The electronic journal of combinatorics
%D 2013
%V 20
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/2264/
%R 10.37236/2264
%F 10_37236_2264
Sarada Herke; Barbara Maenhaut. Perfect 1-factorisations of circulants with small degree. The electronic journal of combinatorics, Tome 20 (2013) no. 1. doi: 10.37236/2264
