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MiS Preprint

Cores, shell indices and the degeneracy of a graph limit

Johannes Rauh


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.

MSC Codes:
graph limit, shell index, graph core, graph degeneracy

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2018 Repository Open Access
Johannes Rauh

Cores, shell indices and the degeneracy of a graph limit