Cores, shell indices and the degeneracy of a graph limit
Combinatorics
2018-05-11 v1
Abstract
The -core of a graph is the maximal subgraph in which every node has degree at least~, the shell index of a node is the largest such that the -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.
Keywords
Cite
@article{arxiv.1805.03736,
title = {Cores, shell indices and the degeneracy of a graph limit},
author = {Johannes Rauh},
journal= {arXiv preprint arXiv:1805.03736},
year = {2018}
}
Comments
11 pages including appendix, no figure