Forest Cuts in Sparse Graphs
Combinatorics
2024-09-27 v1
Abstract
We propose the conjecture that every graph of order with less than edges has a vertex cut that induces a forest. Maximal planar graphs do not have such vertex cuts and show that the density condition would be best possible. We verify the conjecture for planar graphs and show that every graph of order with less than edges has a vertex cut that induces a forest.
Cite
@article{arxiv.2409.17724,
title = {Forest Cuts in Sparse Graphs},
author = {Vsevolod Chernyshev and Johannes Rauch and Dieter Rautenbach},
journal= {arXiv preprint arXiv:2409.17724},
year = {2024}
}