Subgraph statistics in subcritical graph classes1. Issue 4 (10th April 2017)

• Record Type: Journal Article
• Authors: Drmota, Michael; Ramos, Lander; Rué, Juanjo
• Is Part Of: Random structures & algorithms. Volume 51:Issue 4(2017)
• Page Start: 631
• Page End: 673
• Publication Date: 2017-04-10
• Subjects: analytic combinatorics -- generating functions -- random graphs -- subcritical graph classes -- series‐parallel graphs; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20721
• Languages: English
• ISSNs: 1042-9832

Abstract

Abstract: Let H be a fixed graph and G a subcritical graph class. In this paper we show that the number of occurrences of H (as a subgraph) in a graph in G of order n, chosen uniformly at random, follows a normal limiting distribution with linear expectation and variance. The main ingredient in our proof is the analytic framework developed by Drmota, Gittenberger and Morgenbesser to deal with infinite systems of functional equations [Drmota, Gittenberger, and Morgenbesser, Submitted]. As a case study, we obtain explicit expressions for the number of triangles and cycles of length 4 in the family of series‐parallel graphs. © 2017 Wiley Periodicals, Inc. Random Struct. Alg., 51, 631–673, 2017