2 problems

Let $G$ be a fullerene graph on $n$ vertices, meaning a cubic bridgeless plane graph whose faces have size $5$ or $6$. An odd cycle transversal is a set of edges whose removal make…

Let $G$ be a triangle-free graph on $n$ vertices. An odd cycle transversal is a set of edges whose removal makes $G$ bipartite. Erdős's conjecture. Every such graph has an odd cycl…