Journal of Graph Algorithms and Applications
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Special Issue on Graph Drawing Beyond Planarity
A First Order Logic Definition of Beyond-Planar Graphs
Franz J. Brandenburg
Vol. 22, no. 1, pp. 51-66, 2018. Regular paper.
Abstract Beyond-planarity is a collective term for classes of graphs that extend the planar graphs and are defined by drawings with restrictions on crossings. Examples are 1-planar, fan-planar, fan-crossing free, and quasi-planar graphs. We define these and other classes of beyond-planar graphs by simple first order formulas, using two predicates to express a crossing and an adjacency of two edges, and establish inclusion relationships between the so obtained graph classes.
Submitted: May 2017.
Reviewed: August 2017.
Revised: September 2017.
Accepted: October 2017.
Final: October 2017.
Published: January 2018.