On the family of $r$-regular graphs with Grundy number $r+1$

Nicolas Gastineau, Hamamache Kheddouci, Olivier Togni

The Grundy number of a graph $G$, denoted by $\Gamma (G)$, is the largest $k$ such that there exists a partition of $V(G)$, into $k$ independent sets $V_1,\dots ,V_k$ and every vertex o…