Forest cuts in sparse graphs
Vsevolod Chernyshev, Johannes Rauch, Dieter Rautenbach · Discrete Mathematics · 2025
We consider the conjecture that every graph G of order n 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 G of order n with less than edges has a vertex cut that induces a forest.