Odd-ordered Cayley graphs satisfy Erdős--Gyárfás
Michael C. Burkhart
Abstract
Erdős and Gyárfás conjectured that every graph with minimum degree at least three contains a power-of-two-length cycle. We prove every Cayley graph of odd order satisfies the conjecture. As a corollary, we find that Cayley graphs of finite nilpotent groups satisfy the conjecture as well.
Create a lesson
Related papers
A face polynomial invariant for embedded graphs
Hongxia Ma, Metrose Metsidik
The Maximum Second Zagreb Spectral Radius of Trees, Unicyclic Graphs and Bicyclic Graphs
Juan Wang, Genjie Wang
A Low-Diameter Nash-Williams--Tutte Theorem
Pin-Hsian Lee, Peng-Ting Lin, Meng-Tsung Tsai et al.
A Short Proof and Generalization of the Rainbow Cycle Theorem and Improved Bounds for Binary Even-Query LCCs
Andrew D. Lin
Automaticity of structural defects in fixed points of block substitutions
Lior Tenenbaum
Two-block paths in oriented graphs under the Ore-type condition
Ke Zhao, Jia Zhou, Yunshu Gao