English

Quintic graphs with every edge in a triangle

Combinatorics 2021-07-09 v1

Abstract

We characterise the quintic (i.e. 5-regular) multigraphs with the property that every edge lies in a triangle. Such a graph is either from a set of small graphs or is formed by adding a perfect matching to a line graph of a cubic graph as double edges, or can be reduced by a sequence of operations to one of these graphs.

Keywords

Cite

@article{arxiv.2107.04006,
  title  = {Quintic graphs with every edge in a triangle},
  author = {James Preen},
  journal= {arXiv preprint arXiv:2107.04006},
  year   = {2021}
}

Comments

32 pages, 33 figures, 1 table

R2 v1 2026-06-24T04:00:49.674Z