2020/04/03 by Lochlan Brick, Brick, Lochlan, Pu Gao +3
Computer Science · Mathematics · #05C80 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2004.01794
openalex publication_date 2020/04/03 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
We give sufficient conditions under which a random graph with a specified degree sequence is symmetric or asymmetric. In the case of bounded degree sequences, our characterisation captures the phase transition of the symmetry of the random graphs. This phase transition coincides with that of the graph connectivity. However, when the maximum degree is a growing function as the number of vertices tends to infinity, our results suggest that these two thresholds do not coincide any more