Exact square coloring of subcubic planar graphs

We study the exact square chromatic number of subcubic planar graphs. An coloring a graph G is vertex-coloring in which any two vertices at distance exactly 2 receive distinct colors. The smallest colors used such its number, denoted ?[?2](G). This notion related to other types distance-based colorings, as well injective coloring. Indeed, for triangle-free graphs, and coincide. prove tight bounds on special subclasses graphs: bipartite graphs K4-minor-free have most 4. then turn our attention class fullerene are cubic with face sizes 5 6. characterize 3. Furthermore, supporting conjecture Chen, Hahn, Raspaud Wang (that all injectively 5-colorable) we that induced subgraph has 5. done by first proving minimum counterexample be 80 computationally verifying claim