Regular $K_3$-irregular graphs
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915408567599104 |
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| author | Hak, Artem Kozerenko, Sergiy Serdiuk, Andrii |
| author_facet | Hak, Artem Kozerenko, Sergiy Serdiuk, Andrii |
| contents | We address the problem proposed by Chartrand, Erdős and Oellermann (1988) about the existence of regular $K_3$-irregular graphs. We first establish bounds on the $K_3$-degrees of such graphs and use them to prove that there are no such graphs with regularities at most $7$. For the regularity $8$, we narrow down the bounds on the order of such graphs to six possible values. We then present an explicit example of a $9$-regular $K_3$-irregular graph. Finally, we discuss an evolutionary algorithm developed to discover more examples of $r$-regular $K_3$-irregular graphs for consecutive values $r \in \{9, \dots, 30\}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18776 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regular $K_3$-irregular graphs Hak, Artem Kozerenko, Sergiy Serdiuk, Andrii Combinatorics Discrete Mathematics 05C07, 05C99, 68T20 We address the problem proposed by Chartrand, Erdős and Oellermann (1988) about the existence of regular $K_3$-irregular graphs. We first establish bounds on the $K_3$-degrees of such graphs and use them to prove that there are no such graphs with regularities at most $7$. For the regularity $8$, we narrow down the bounds on the order of such graphs to six possible values. We then present an explicit example of a $9$-regular $K_3$-irregular graph. Finally, we discuss an evolutionary algorithm developed to discover more examples of $r$-regular $K_3$-irregular graphs for consecutive values $r \in \{9, \dots, 30\}$. |
| title | Regular $K_3$-irregular graphs |
| topic | Combinatorics Discrete Mathematics 05C07, 05C99, 68T20 |
| url | https://arxiv.org/abs/2507.18776 |