# Bounding the number of cycles in a graph in terms of its degree sequence

## TL;DR

This paper establishes an upper bound on the number of cycles in a simple graph based on its degree sequence, resolving existing conjectures and improving bounds for planar graphs.

## Contribution

It introduces a new bound relating cycle count to degree sequence and applies it to settle conjectures and enhance bounds in planar graph theory.

## Key findings

- Resolved several conjectures on cycle counts
- Provided tighter bounds for planar graphs
- Established a relation between degree sequence and cycle number

## 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.