The confirmation of a conjecture on disjoint cycles in a graph

TL;DR

This paper proves a conjecture stating that large graphs with a certain degree sum condition contain a specified number of disjoint cycles, advancing understanding in graph theory.

Contribution

It confirms a conjecture by Gould, Hirohata, and Keller regarding disjoint cycles in graphs with large order and degree sum conditions.

Findings

Proves the conjecture for sufficiently large graphs.

Establishes a degree sum threshold for disjoint cycles.

Extends previous results in graph cycle theory.

Abstract

In this paper, we prove the following conjecture proposed by Gould, Hirohata and Keller [Discrete Math. submitted]: Let $G$ be a graph of sufficiently large order. If $\sigma_t(G) \geq 2kt - t + 1$ for any two integers $k \geq 2$ and $t \geq 5$, then $G$ contains $k$ disjoint cycles.