Bounding the number of cycles in a graph in terms of its degree sequence
Combinatorics
2019-07-30 v1
Abstract
We give an upper bound on the number of cycles in a simple graph in terms of its degree sequence, and apply this bound to resolve several conjectures of Kir\'aly and Arman and Tsaturian and to improve upper bounds on the maximum number of cycles in a planar graph.
Cite
@article{arxiv.1907.12091,
title = {Bounding the number of cycles in a graph in terms of its degree sequence},
author = {Zdeněk Dvořák and Natasha Morrison and Jonathan A. Noel and Sergey Norin and Luke Postle},
journal= {arXiv preprint arXiv:1907.12091},
year = {2019}
}