The O'Donnell graphs are a set of graphs on 40, 46, and 56 vertices (together with a graph on 15 vertices used to construct the 40-vertex graph) that are unit-distance with chromatic number 4 and girth 4. For a time, these (together with the Chilakamarri moth graph) were the (reverse) incrementally smallest known such graph. They were subsequently been supplanted by the Hochberg-O'Donnell fish graph and finally in the (presumed to be smallest possible) 17-vertex Exoo-Ismailescu graph.
