English

Triangle-Free Penny Graphs: Degeneracy, Choosability, and Edge Count

Discrete Mathematics 2018-10-03 v1 Combinatorics

Abstract

We show that triangle-free penny graphs have degeneracy at most two, list coloring number (choosability) at most three, diameter D=Ω(n)D=\Omega(\sqrt n), and at most min(2nΩ(n),2nD2)\min\bigl(2n-\Omega(\sqrt n),2n-D-2\bigr) edges.

Keywords

Cite

@article{arxiv.1708.05152,
  title  = {Triangle-Free Penny Graphs: Degeneracy, Choosability, and Edge Count},
  author = {David Eppstein},
  journal= {arXiv preprint arXiv:1708.05152},
  year   = {2018}
}

Comments

10 pages, 2 figures. To appear at the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017)

R2 v1 2026-06-22T21:16:50.275Z