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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
36/2018

Cores, shell indices and the degeneracy of a graph limit

Johannes Rauh

Abstract

The $k$-core of a graph is the maximal subgraph in which every node has degree at least $k$, the shell index of a node is the largest $k$ such that the $k$-core contains the node, and the degeneracy of a graph is the largest shell index of any node. After a suitable normalization, these three concepts generalize to limits of dense graphs (also called graphons). In particular, the degeneracy is continuous with respect to the cut metric.

Received:
16.05.18
Published:
24.05.18
MSC Codes:
05CXX
Keywords:
graph limit, shell index, graph core, graph degeneracy

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Preprint
2018 Repository Open Access
Johannes Rauh

Cores, shell indices and the degeneracy of a graph limit