Cycles of Length 4 or 8 in Graphs with Diameter 2 and Minimum Degree at Least 3
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914292579696640 |
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| author | Carr, Avery |
| author_facet | Carr, Avery |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19302 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cycles of Length 4 or 8 in Graphs with Diameter 2 and Minimum Degree at Least 3 Carr, Avery Combinatorics 05C38, 05C35, 05C75, 05C12 G.2.2 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. |
| title | Cycles of Length 4 or 8 in Graphs with Diameter 2 and Minimum Degree at Least 3 |
| topic | Combinatorics 05C38, 05C35, 05C75, 05C12 G.2.2 |
| url | https://arxiv.org/abs/2508.19302 |