Roman Domination on Graphings
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909190551764992 |
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| author | Rettich, Adrian |
| author_facet | Rettich, Adrian |
| contents | We study a variant of domination, called Roman domination, where we must assign to each vertex one of the labels 0, 1, or 2 and require that every vertex with label 0 has a neighbour with label 2. We study the problem of finding a low-cost Roman dominating function on Lebesgue-measurable graphings, that is, on infinite graphs whose vertices are the points of a probability space. We provide a framework to tackle optimisation problems in the measurable combinatorial setting. In particular, we fully answer the Roman domination problem on irrational cycle graphs, a specific type of graphing on the space $\mathbb{R}/\mathbb{Z}$ where an irrational number $α$ is given and two vertices are adjacent if and only if their distance is $α$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19718 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Roman Domination on Graphings Rettich, Adrian Combinatorics Functional Analysis We study a variant of domination, called Roman domination, where we must assign to each vertex one of the labels 0, 1, or 2 and require that every vertex with label 0 has a neighbour with label 2. We study the problem of finding a low-cost Roman dominating function on Lebesgue-measurable graphings, that is, on infinite graphs whose vertices are the points of a probability space. We provide a framework to tackle optimisation problems in the measurable combinatorial setting. In particular, we fully answer the Roman domination problem on irrational cycle graphs, a specific type of graphing on the space $\mathbb{R}/\mathbb{Z}$ where an irrational number $α$ is given and two vertices are adjacent if and only if their distance is $α$. |
| title | Roman Domination on Graphings |
| topic | Combinatorics Functional Analysis |
| url | https://arxiv.org/abs/2404.19718 |