What question did this study set out to answer?

The goal is to establish the relationship between graph connectivity and the longest cycles in 5-connected graphs.

December 21, 2025Discrete Mathematics Algorithms and Applications0 citations

Longest cycles in 5-connected graphs

XLXia LiChongqing Jiaotong University YXYinghui XuNanjing University of Science and Technology JCJunqing CaiTianjin Normal University

Key Points

The goal is to establish the relationship between graph connectivity and the longest cycles in 5-connected graphs.
Proof of graph properties related to 5-connectivity.
Application of Dirac's theorem to establish bounds on cycles.
Analysis of specific vertex configurations.
Demonstrated that the circumference of a 5-connected graph is influenced by minimum degree.
Established new bounds based on prior work of Cai, Li, and Sun.

Abstract

Let Formula: see text is an independent set of Formula: see textFormula: see text. According to a theorem of Dirac, which states that if Formula: see text is a Formula: see text-connected graph on Formula: see text vertices and minimum degree Formula: see text, then the circumference Formula: see text, Cai, Li and Sun proved that if Formula: see text is a Formula: see text-connected graph on Formula: see text vertices, then Formula: see text. In this paper, we prove that if Formula: see text is a Formula: see text-connected graph on Formula: see text vertices, then Formula: see text.

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