Counterexamples to Gerbner's Conjecture on Stability of Maximal $F$-free Graphs

Jian Wang, Shipeng Wang, Weihua Yang

Let $F$ be an $(r+1)$-color critical graph with $r\ge 2$, that is, $\chi (F)=r+1$ and there is an edge $e$ in $F$ such that $\chi (F-e)=r$. Gerbner recently conjectured that every $n$-ver…