A new bound for Vizing's conjecture

Elliot Krop, Kimber Wolff

For any graph $G$, we define the power $\ddot{I}€(G)$ as the minimum of the largest number of neighbors in a ${\hat{I}}^3$-set of $G$, of any vertex, taken over all ${\hat{I}}^3$-sets of $G$. We show that…