On Vizing's problem for triangle-free graphs

Ross J. Kang, Matthieu Rosenfeld

We prove that $\ddot{I}‡(G)\le \lceil (\hat{I}”+1)/2\rceil +1$ for any triangle-free graph $G$ of maximum degree $\hat{I}”$ provided $\hat{I}”\ge 524$. This gives tangible progress towards an old problem o…