Eroh–Kang–Yi cycle-rank conjecture for metric dimension and zero forcing

Let $G$ be a connected graph. Write $Z(G)$ for its zero forcing number, let $\dim(G)$ denote its metric dimension, and let $c(G)$ be the number of edges that must be removed from $G$ to obtain a forest. Cycle-rank conjecture.

$$\dim(G) \leq Z(G)+c(G).$$

This conjecture compares two graph parameters and is known for trees and graphs with one cycle. The paper proves a weaker bound, so the conjecture remains open in the stated generality.