A note on sequences variant of irregularity strength for hypercubes
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914827061952512 |
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| author | Flaszczyńska, Anna Gorzkowska, Aleksandra Woźniak, Mariusz |
| author_facet | Flaszczyńska, Anna Gorzkowska, Aleksandra Woźniak, Mariusz |
| contents | Let $f: E \mapsto \{1,2,\dots,k\}$ be an edge coloring of the $n$ - dimensional hypercube $H_n$. By the palette at a vertex $v$ we mean the sequence $\left(f(e_1(v)), f(e_1(v)),\dots, f(e_n(v))\right)$, where $e_i(v)$ is the $i$ - dimensional edge incident to $v$. In the paper, we show that two colors are enough to distinguish all vertices of the $n$ - dimensional hypercube $H_n$ ($n \geq 2$) by their palettes. We also show that if $f$ is a proper edge coloring of the hypercube $H_n$ ($n\geq 5$), then $n$ colors suffice to distinguish all vertices by their palettes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03612 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on sequences variant of irregularity strength for hypercubes Flaszczyńska, Anna Gorzkowska, Aleksandra Woźniak, Mariusz Combinatorics 05C15, 05C78 Let $f: E \mapsto \{1,2,\dots,k\}$ be an edge coloring of the $n$ - dimensional hypercube $H_n$. By the palette at a vertex $v$ we mean the sequence $\left(f(e_1(v)), f(e_1(v)),\dots, f(e_n(v))\right)$, where $e_i(v)$ is the $i$ - dimensional edge incident to $v$. In the paper, we show that two colors are enough to distinguish all vertices of the $n$ - dimensional hypercube $H_n$ ($n \geq 2$) by their palettes. We also show that if $f$ is a proper edge coloring of the hypercube $H_n$ ($n\geq 5$), then $n$ colors suffice to distinguish all vertices by their palettes. |
| title | A note on sequences variant of irregularity strength for hypercubes |
| topic | Combinatorics 05C15, 05C78 |
| url | https://arxiv.org/abs/2406.03612 |