The Hochberg-O'Donnell fish graph is the unit-distance graph on 23 nodes and 42 edges illustrated above. It is triangle-free
and is the smallest example of a unit-distance
4-chromatic graph with girth 4 listed by Soifer (2016,
p. 445).
Exoo, G. and Ismailescu, D. "Small Order Triangle-Free 4-Chromatic Unit Distance Graphs." Geombinatorics26, 49-64, 2016.Hochberg,
R. and O'Donnell, P. "Some 4-Chromatic Unit-Distance Graphs Without Small Cycles."
Geombinatorics5, 137-141, 1996.Soifer, A. Open
Problems in Mathematics (Ed. J. F. Nash, Jr. and M. Th. Rassias).
Switzerland: Springer, p. 445, 2016.Taxel, P. "Are 4-Chromatic
3-Connected Unit Distance Graphs Always Rigid?" Dec. 25, 2020. https://math.stackexchange.com/questions/3958839/are-4-chromatic-3-connected-unit-distance-graphs-always-rigid.