**Selected open problems in graph drawing**.

F. J. Brandenburg, D. Eppstein, M. T. Goodrich, S. G. Kobourov, G. Liotta, and P. Mutzel.

11th Int. Symp. Graph Drawing, Perugia, Italy, 2003.

Springer,*Lecture Notes in Comp. Sci.*2912, 2004, pp. 515–539.We survey a number of open problems in theoretical and applied graph drawing.

**On the density of maximal 1-planar graphs**.

F. J. Brandenburg, D. Eppstein, A. Gleißner, M. T. Goodrich, K. Hanauer, and J. Reislhuber.

*20th Int. Symp. Graph Drawing*, Redmond, Washington, 2012.

Springer,*Lecture Notes in Comp. Sci.*7704, 2013, pp. 327–338.

A graph is 1-planar if it can be drawn in the plane with at most one crossing per edge, and maximal 1-planar if it is 1-planar but adding any edge would force more than one crossing on some edge or edges. Although maximal 1-planar graphs on

*n*vertices may have as many as 4*n*− 8 edges, we show that there exist maximal 1-planar graphs with as few as 45*n*/17 + O(1) edges.

Co-authors – Publications – David Eppstein – Theory Group – Inf. & Comp. Sci. – UC Irvine

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