The threshold of symmetry in random graphs with specified degree sequences
Combinatorics
2020-04-07 v1
Abstract
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
Keywords
Cite
@article{arxiv.2004.01794,
title = {The threshold of symmetry in random graphs with specified degree sequences},
author = {Lochlan Brick and Pu Gao and Angus Southwell},
journal= {arXiv preprint arXiv:2004.01794},
year = {2020}
}
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22 pages