On t-colorable k-plane drawings

Miriam Goetze; Michael Kaufmann; Soeren Terziadis

On t-colorable k-plane drawings

Combinatorics 2026-07-28 v1

Authors: Miriam Goetze , Michael Kaufmann , Soeren Terziadis

Abstract

In this work, we introduce $t$ -colorable $k$ -plane drawings, that is, drawings of graphs with a $t$ -edge-coloring where every edge is crossed by at most $k$ edges of each color. We give tight upper bounds on the edge- and crossing density for small values of $t$ and $k$ and show that the recognition of such drawings is NP-complete if $t\geq 2$ and $k\geq1$ .

Cite

@article{arxiv.2607.25682,
  title  = {On t-colorable k-plane drawings},
  author = {Miriam Goetze and Michael Kaufmann and Soeren Terziadis},
  journal= {arXiv preprint arXiv:2607.25682},
  year   = {2026}
}