Generating Labeled Planar Graphs Uniformly at Random

Abstract. We present an expected polynomial time algorithm to generate a labeled planar graph uniformly at random. To generate the planar graphs, we derive recurrence formulas that count all such graphs with E vertices and F edges, based on a decomposition into 1-, 2-, and 3-connected components. For 3-connected graphs we apply a recent random generation algorithm by Schaeffer and a counting formula by Mullin and Schellenberg.

• Type: Conference
• Year: 2003
• Where: ICALP
• Authors: Manuel Bodirsky, Clemens Gröpl, Mihyun Kang
• Keywords: ICALP 2003, Planar Graphs, Polynomial Time Algorithm, Random Generation Algorithm, Theoretical Computer Science