Year: 2019
Type: preprint
Abstract: 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 $k\geq 12$.
Source: arXiv (Cornell University)
Authors: Lyngsie, Kasper S., Merker, Martin
Institution: Technical University of Denmark
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2937212271