English

Cores, shell indices and the degeneracy of a graph limit

Combinatorics 2018-05-11 v1

Abstract

The kk-core of a graph is the maximal subgraph in which every node has degree at least~kk, the shell index of a node is the largest kk such that the kk-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