• Corpus ID: 245144909

# Limit of connected multigraph with fixed degree sequence

@inproceedings{BlancRenaudie2021LimitOC,
title={Limit of connected multigraph with fixed degree sequence},
author={Arthur Blanc-Renaudie},
year={2021}
}
Motivated by the scaling limits of the connected components of the configuration model, we study uniform connected multigraphs with fixed degree sequence D and with surplus k. We call those random graphs (D, k)-graphs. We prove that, for every k ∈ N, under natural conditions of convergence of the degree sequence, (D, k)-graphs converge toward either (P , k)-graphs or (Θ, k)-ICRG (inhomogeneous continuum random graphs). We prove similar results for (P , k)-graphs and (Θ, k)-ICRG, which have…
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