A number of graphs are associated with Geoffrey Exoo and Dan Ismailescu.

The graphs on 17, 19, and 21 vertices (Exoo and Ismailescu 2016, Soifer 2024) are examples of small triangle-freeunit-distance
graphs with chromatic number 4 and girth
4. These improve on larger examples previously found by O'Donnell, Chilakamarri,
and Hochberg between 1994 and 1996, as summarized by Soifer (2008, Table 15.1, p. 445)
and Soifer (2024, Table 15.1, p. 145) and reproduced below. Moreover, there
is evidence that no smaller such graph exist (Soifer 2024). The 17-vertex Exoo-Ismailescu
graph decorates the front cover of the October 2016 issue of Geombinatorics.

Chilakamarri, K. "A 4-Chromatic Unit Distance Graph With No Triangles." Geomcombinatorics4, No. 3, 64-76, 1995.Exoo,
G. and Ismailescu, D. "Small Order Triangle-Free 4-Chromatic Unit Distance Graphs."
Geombinatorics26, No. 2, 49-64, 2016.Exoo, G. and
Ismailescu, D. "The Chromatic Number of the Plane Is at Least 5--A New Proof."
1 May 2018. https://arxiv.org/abs/1805.00157.Exoo,
G. and Ismailescu, D. "A 6-Chromatic Two-Distance Graph in the Plane."
29 Sep 2019. https://arxiv.org/abs/1909.13177.Hochberg,
R. and O'Donnell, P. "Some 4-Chromatic Unit-Distance Graphs Without Small Cycles."
Geombinatorics5, 137-141, 1996.Kiteck, D. and Payne,
K. "A 21-Vertex 4-Chromatic Unit-Distance Graph of Girth 4." Ball State
Undergraduate Mathematics Exchange15, No. 1, 2-9, 2021.O'Donnell,
P. "A Triangle-Free 4-Chramatic Graph in the Plane." Geombinatorics4,
No. 1, 23-29, 1994.O'Donnell, P. "A 40 Vertex 4-Chromatic
Triangle-Free Unit Distance Graph." Geombinatorics5, No. 1,
30-34, 1995.Soifer, A. The
Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of Its
Creators. New York: Springer, 2008.Soifer, A. "Exoo-Ismailescu:
The Final Word on Problem 15.4." Ch. 16 in The
New Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of
Its Creators, 2nd ed. New York: Springer, pp. 147-160, 2024.Wormald,
N. C. "A 4-Chromatic Graph With a Special Plane Drawing." J. Austral.
Math. Soc.28, 1-8, 1979.