On the biplanarity of blowups.
D. Eppstein.
arXiv:2301.09246.
Proc. 31st Int. Symp. Graph Drawing and Network Visualization, Palermo, Italy, 2023 (best paper award).
Springer, Lecture Notes in Computer Science 14465 (part I), pp. 3–17, doi:10.1007/978-3-031-49272-3_1.
J. Graph Algorithms &
Applications 28 (2): 83–99, 2024, doi:10.7155/jgaa.v28i2.2989.
Expanding every vertex of a planar graph to two independent copies can produce a graph of thickness greater than two, disproving a conjecture of Ellen Gethner. We also investigate special cases of this construction for which the thickness is two, such as the graphs whose edges can be decomposed into a path and a dual path.