Regular graphs are universally 3-edge-weightable
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910020851990528 |
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| author | Deng, Kecai |
| author_facet | Deng, Kecai |
| contents | A graph is universally $k$-edge-weightable if for every $k$-element set $Q\subset\mathbb{R}$, it admits a proper $Q$-edge weighting. The settled 1-2-3 conjecture implies that for any arithmetic progression $\{a,b,c\}$, every nice regular graph has a proper $\{a,b,c\}$-edge weighting. We prove that this remains valid for all 3-element set $\{a,b,c\}$ with $c-b \neq b-a$. Consequently, every nice regular graph is universally $3$-edge-weightable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06659 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Regular graphs are universally 3-edge-weightable Deng, Kecai Combinatorics 05C15, 05C78 A graph is universally $k$-edge-weightable if for every $k$-element set $Q\subset\mathbb{R}$, it admits a proper $Q$-edge weighting. The settled 1-2-3 conjecture implies that for any arithmetic progression $\{a,b,c\}$, every nice regular graph has a proper $\{a,b,c\}$-edge weighting. We prove that this remains valid for all 3-element set $\{a,b,c\}$ with $c-b \neq b-a$. Consequently, every nice regular graph is universally $3$-edge-weightable. |
| title | Regular graphs are universally 3-edge-weightable |
| topic | Combinatorics 05C15, 05C78 |
| url | https://arxiv.org/abs/2602.06659 |