Author

J. Goedgebeur

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Preprint Aug 2026

Counterexamples to the Albertson-Berman conjecture: minimum order, connectivity and an improved ratio bound

In 1979, Albertson and Berman conjectured that every planar graph $G$ contains an induced forest of order at least $|V(G)|/2$. This long-standing conjecture was recently disproved by several explicit counterexamples, which naturally led to several extremal and structural questions that we answer. We combine mathematica...

W. Cames van Batenburg, J. Goedgebeur, Jorik Jooken · 0 citations

Preprint Aug 2026

Disproving the Petersen Coloring Conjecture: Theoretical Analysis and an Infinite Family of Counterexamples

In 1988, Jaeger conjectured that every bridgeless cubic graph $G$ admits a Petersen coloring; that is, a map $E(G) \to E(P)$ mapping any two adjacent edges of $G$ to two adjacent edges of the Petersen graph $P$. A positive resolution to Jaeger's conjecture would have immediately resolved several other famous and long-s...

J. Goedgebeur, Jorik Jooken, Edita Máčajová et al. · 0 citations