Reconfiguration graphs for minimal domination sets
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910683740766208 |
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| author | Beaton, Iain |
| author_facet | Beaton, Iain |
| contents | A dominating set $S$ in a graph is a subset of vertices such that every vertex is either in $S$ or adjacent to a vertex in $S$. A minimal dominating set $M$ is a dominating set such that $M-v$ is not a dominating set for all $v \in M$. In this paper we introduce a reconfiguration graph $\mathcal{R}(G)$ for minimal dominating sets under a generalization of the token sliding model. We give some preliminary results which include showing that $\mathcal{R}(G)$ is connected for trees and split graphs. Additionally we classify all graphs which have $\mathcal{R}(G) = K_n$ and $\mathcal{R}(G) = \overline{K_n}$ for all $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02300 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reconfiguration graphs for minimal domination sets Beaton, Iain Combinatorics A dominating set $S$ in a graph is a subset of vertices such that every vertex is either in $S$ or adjacent to a vertex in $S$. A minimal dominating set $M$ is a dominating set such that $M-v$ is not a dominating set for all $v \in M$. In this paper we introduce a reconfiguration graph $\mathcal{R}(G)$ for minimal dominating sets under a generalization of the token sliding model. We give some preliminary results which include showing that $\mathcal{R}(G)$ is connected for trees and split graphs. Additionally we classify all graphs which have $\mathcal{R}(G) = K_n$ and $\mathcal{R}(G) = \overline{K_n}$ for all $n$. |
| title | Reconfiguration graphs for minimal domination sets |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2411.02300 |