Cycles of Length 4 or 8 in Graphs with Diameter 2 and Minimum Degree at Least 3

In this short note it is shown that every graph of diameter 2 and minimum degree at least 3 contains a cycle of length 4 or 8. This result contributes to the study of the Erdős-Gyárfás Conjecture by confirming it for the class of diameter-2 graphs.

Publication Details

Journal
ArXiv.org
Published
2025-08-25
Primary Topic
Geochemistry and Geologic Mapping
Type
article
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article

Cycles of Length 4 or 8 in Graphs with Diameter 2 and Minimum Degree at Least 3

ArXiv.org
Geochemistry and Geologic Mapping
article

Cycles of Length 4 or 8 in Graphs with Diameter 2 and Minimum Degree at Least 3

article en

Abstract

In this short note it is shown that every graph of diameter 2 and minimum degree at least 3 contains a cycle of length 4 or 8. This result contributes to the study of the Erdős-Gyárfás Conjecture by confirming it for the class of diameter-2 graphs.

ArXiv.org
Openalex Percentile: Top 60%
Geochemistry and Geologic Mapping
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Cycles of Length 4 or 8 in Graphs with Diameter 2 and Minimum Degree at Least 3 · ArXiv.org (2025) | TGRS Research Map | TGRS