Partitioning a Planar Graph into two Triangle-Forests
Combinatorics
2024-10-21 v3 Discrete Mathematics
Abstract
We show that the vertices of every planar graph can be partitioned into two sets, each inducing a so-called triangle-forest, i.e., a graph with no cycles of length more than three. We further discuss extensions to locally planar graphs. After finishing the paper we noticed that our main result was already proved much earlier by Carsten Thomassen [Decomposing a Planar Graph into Degenerate Graphs, JCTB 1995].
Keywords
Cite
@article{arxiv.2401.15394,
title = {Partitioning a Planar Graph into two Triangle-Forests},
author = {Kolja Knauer and Clément Rambaud and Torsten Ueckerdt},
journal= {arXiv preprint arXiv:2401.15394},
year = {2024}
}
Comments
8 pages, 3 figures, main result already proved by Carsten Thomassen [Decomposing a Planar Graph into Degenerate Graphs, JCTB 1995]