Work

Forest cuts in sparse graphs

Year: 2025

Type: article

Abstract: 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.

Source: Discrete Mathematics

DOI: 10.1016/j.disc.2025.114594

Authors: Vsevolod Chernyshev, Johannes Rauch, Dieter Rautenbach

Institutions: Centre National de la Recherche Scientifique, Université Clermont Auvergne, Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes, Clermont Auvergne INP, Universität Ulm

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,320

Funder: Deutsche Forschungsgemeinschaft