Jacobsthal numbers in generalised Petersen graphs

Henning Bruhn; Laura Gellert; Jacob Günther

Jacobsthal numbers in generalised Petersen graphs

Combinatorics 2015-03-12 v1

Authors: Henning Bruhn , Laura Gellert , Jacob Günther

Abstract

We prove that the number of $1$ -factorisations of a generalised Petersen graph of the type $GP(3k,k)$ is equal to the $k$ th Jacobsthal number $J(k)$ if $k$ is odd, and equal to $4J(k)$ , when $k$ is even. Moreover, we verify the list colouring conjecture for $GP(3k,k)$ .

Cite

@article{arxiv.1503.03390,
  title  = {Jacobsthal numbers in generalised Petersen graphs},
  author = {Henning Bruhn and Laura Gellert and Jacob Günther},
  journal= {arXiv preprint arXiv:1503.03390},
  year   = {2015}
}

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12 pages

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