On the density of maximal 1-planar graphs
GD'12 Proceedings of the 20th international conference on Graph Drawing
Testing maximal 1-planarity of graphs with a rotation system in linear time
GD'12 Proceedings of the 20th international conference on Graph Drawing
A linear time algorithm for testing maximal 1-planarity of graphs with a rotation system
Theoretical Computer Science
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In this paper, we examine the re-embeddability of maximum 1-planar graphs. In particular, we prove that every optimal 1-planar graph is uniquely 1-embeddable on the sphere except for a sequence of graphs that are minimal with respect to certain reductions. These optimal 1-planar graphs are closely related to their quadrangular subgraphs. We also give a generating theorem for optimal 1-planar graphs.