David Eppstein – Publications

Publications with Franz-Josef Brandenburg

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