A First Order Logic Definition of Beyond-Planar Graphs

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.