Sparse random planar graphs

This is a survey article on the research area of sparse random planar graphs. We first review some of the important results from the classical theory of random graphs and then consider the so-called core-kernel approach. This method allows to analyse random planar graphs via the Pólya urn model, Prüfer sequences, and the balls–into-bins model. Finally, we discuss some recent results on longest and shortest cycles and the maximum degree in sparse random planar graphs.