McDiarmid–Reed conjecture for triangle-free induced subgraphs of the triangular lattice

Let $G$ be a triangle-free induced subgraph of the triangular lattice, and let $b$ be a positive integer. The graph $G$ is $(a,b)$-colorable if, when every vertex receives the same list of $a$ colors, one can choose $b$ colors at each vertex so that adjacent vertices receive disjoint color sets.

McDiarmid–Reed conjecture. Every triangle-free induced subgraph of the triangular lattice is

$$\left(\left\lceil\frac{9b}{4}\right\rceil,b\right)\text{-colorable}.$$

This conjecture concerns multicoloring for radio-frequency assignment on triangular-lattice networks. The source gives no resolution status; the paper proves the related list-coloring bound $(5m,2m)$ for finite triangle-free induced subgraphs, rather than the stated ordinary-coloring conjecture.