Let $G$ be a connected graph with an even number of edges. We show that if the subgraph of $G$ induced by the vertices of odd degree has a perfect matching, then the line graph of $G$ has a $2$-factor whose connected components are cycles of even length (an even $2$-factor). For a cubic graph $G$, we also give a necessary and sufficient condition so that the corresponding line graph $L(G)$ has an even cycle decomposition of index $3$, i.e., the edge-set of $L(G)$ can be partitioned into three $2$-regular subgraphs whose connected components are cycles of even length. The more general problem of the existence of even cycle decompositions of index $m$ in $2d$-regular graphs is also addressed.
@article{10_37236_5660,
author = {Arrigo Bonisoli and Simona Bonvicini},
title = {Even cycles and even 2-factors in the line graph of a simple graph},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {4},
doi = {10.37236/5660},
zbl = {1373.05097},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5660/}
}
TY - JOUR
AU - Arrigo Bonisoli
AU - Simona Bonvicini
TI - Even cycles and even 2-factors in the line graph of a simple graph
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/5660/
DO - 10.37236/5660
ID - 10_37236_5660
ER -
%0 Journal Article
%A Arrigo Bonisoli
%A Simona Bonvicini
%T Even cycles and even 2-factors in the line graph of a simple graph
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/5660/
%R 10.37236/5660
%F 10_37236_5660
Arrigo Bonisoli; Simona Bonvicini. Even cycles and even 2-factors in the line graph of a simple graph. The electronic journal of combinatorics, Tome 24 (2017) no. 4. doi: 10.37236/5660
