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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2507.15083 |
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| _version_ | 1866915401354444800 |
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| author | Cichacz, Sylwia Krupińska, Barbara Woźniak, Mariusz |
| author_facet | Cichacz, Sylwia Krupińska, Barbara Woźniak, Mariusz |
| contents | Given a finite Abelian group $(A,+)$, consider a tree $T$ with $|A|$ vertices. The labeling $f \colon V (T) \rightarrow A$ of the vertices of some graph $G$ induces an edge labeling in $G$, thus the edge $uv$ receives the label $f (u) + f (v)$.
The tree $T$ is $A$-rainbow colored if $f$ is a bijection and edges have different colors. In this paper, we give necessary and sufficient conditions for a caterpillar with three spine vertices to be $A$-rainbow, when $A$ is an elementary $p$-group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15083 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On rainbow caterpillars in elementary $p$-groups Cichacz, Sylwia Krupińska, Barbara Woźniak, Mariusz Combinatorics Given a finite Abelian group $(A,+)$, consider a tree $T$ with $|A|$ vertices. The labeling $f \colon V (T) \rightarrow A$ of the vertices of some graph $G$ induces an edge labeling in $G$, thus the edge $uv$ receives the label $f (u) + f (v)$. The tree $T$ is $A$-rainbow colored if $f$ is a bijection and edges have different colors. In this paper, we give necessary and sufficient conditions for a caterpillar with three spine vertices to be $A$-rainbow, when $A$ is an elementary $p$-group. |
| title | On rainbow caterpillars in elementary $p$-groups |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2507.15083 |