A proof of the Kotzig-Ringel-Rosa Conjecture
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866909470291918848 |
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| author | Gnang, Edinah K. |
| author_facet | Gnang, Edinah K. |
| contents | In graph theory, a graceful labeling of a graph with m edges is a labeling of its vertices with a subset of the integers ranging from 0 to m inclusive, such that no two vertices share a label, and each edge is uniquely identified by the absolute difference of labels assigned to its endpoints. The Kotzig-Ringel-Rosa conjecture asserts that every tree admits a graceful labeling. We provide a proof of this long standing conjecture via a functional reformulation of the conjecture and a composition lemma. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_03178 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A proof of the Kotzig-Ringel-Rosa Conjecture Gnang, Edinah K. Combinatorics In graph theory, a graceful labeling of a graph with m edges is a labeling of its vertices with a subset of the integers ranging from 0 to m inclusive, such that no two vertices share a label, and each edge is uniquely identified by the absolute difference of labels assigned to its endpoints. The Kotzig-Ringel-Rosa conjecture asserts that every tree admits a graceful labeling. We provide a proof of this long standing conjecture via a functional reformulation of the conjecture and a composition lemma. |
| title | A proof of the Kotzig-Ringel-Rosa Conjecture |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2202.03178 |