Minimum degree conditions for the existence of a sequence of cycles whose lengths differ by one or two

TL;DR

This paper improves upon previous results regarding the existence of specific paths and cycles in graphs, generalizing earlier theorems and settling longstanding conjectures in graph theory.

Contribution

It enhances known conditions for cycle existence with lengths differing by one or two, generalizing prior theorems and resolving conjectures.

Findings

Improved conditions for cycle existence with specified length differences

Generalization of Bondy and Vince's earlier results

Resolution of two famous conjectures by Thomassen

Abstract

Gao, Huo, Liu and Ma (2019) proved a result on the existence of paths connecting specified two vertices whose lengths differ by one or two. By using this result, they settled two famous conjectures due to Thomassen (1983). In this paper, we improve their result, and obtain a generalization of a result of Bondy and Vince (1998).