Geodesic
Cycle lengths modulo $k$ in large 3-connected cubic graphs
Advances in Combinatronics (2021)

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We prove that for all natural numbers $m$ and $k$ where $k$ is odd, there exists a natural number $N(k)$ such that any 3-connected cubic graph with at least $N(k)$ vertices contains a cycle of length $m$ modulo $k$. We also construct a family of graphs showing that this is not true for 2-connected cubic graphs if $m$ and $k$ are divisible by 3 and $k\geq 12$.
Publié le : 
@article{ADVC_2021_a6,
     author = {Kasper S. Lyngsie and Martin Merker},
     title = {Cycle lengths modulo $k$ in large 3-connected cubic graphs},
     journal = {Advances in Combinatronics},
     publisher = {mathdoc},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADVC_2021_a6/}
}
TY  - JOUR
AU  - Kasper S. Lyngsie
AU  - Martin Merker
TI  - Cycle lengths modulo $k$ in large 3-connected cubic graphs
JO  - Advances in Combinatronics
PY  - 2021
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADVC_2021_a6/
LA  - en
ID  - ADVC_2021_a6
ER  - 
%0 Journal Article
%A Kasper S. Lyngsie
%A Martin Merker
%T Cycle lengths modulo $k$ in large 3-connected cubic graphs
%J Advances in Combinatronics
%D 2021
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADVC_2021_a6/
%G en
%F ADVC_2021_a6
Kasper S. Lyngsie; Martin Merker. Cycle lengths modulo $k$ in large 3-connected cubic graphs. Advances in Combinatronics (2021). http://geodesic.mathdoc.fr/item/ADVC_2021_a6/