• Mathematics of computing → Random graphs
• Mathematics of computing → Generating functions
Mihyun Kang
Institute of Discrete Mathematics, Graz University of Technology, Austria
Michael Missethan
Institute of Discrete Mathematics, Graz University of Technology, Austria

Abstract. Let A(n,m) be a graph chosen uniformly at random from the class of all vertex-labelled outerplanar graphs with n vertices and m edges. We consider A(n,m) in the sparse regime when m=n/2+s for s=o(n). We show that with high probability the giant component in A(n,m) emerges at m=n/2+O (n^{2/3}) and determine the typical order of the 2-core. In addition, we prove that if s=ω(n^{2/3}), with high probability every edge in A(n,m) belongs to at most one cycle.