Year: 2026
Type: preprint
Abstract: We prove that there is an absolute constant $c>0$ such that every connected vertex-transitive graph $G$ on $n \ge 3$ vertices contains a cycle of length at least $cn$. Moreover, every such graph with sufficiently large degree $d$ contains a cycle of length at least $(1-d^{-1/100})n$. This gives the first linear bound towards Lovász's Hamiltonicity conjecture. The proof combines a structural result of DeVos and Mohar on vertex-transitive graphs with a general framework for finding long cycles, which may be of independent interest.
Source: arXiv (Cornell University)
Authors: Ma, Jie, Zhao, Ziyuan
Institution: University of Science and Technology of China
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1330075977, G1836446064, G442152759
OpenAlex ID: W7215722501