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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2206.13182 |
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| _version_ | 1866911983033384960 |
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| author | Petr, Jan Portier, Julien Versteegen, Leo |
| author_facet | Petr, Jan Portier, Julien Versteegen, Leo |
| contents | We show that the maximum number of minimum dominating sets of a forest with domination number $γ$ is at most $\sqrt{5}^γ$ and construct for each $γ$ a tree with domination number $γ$ that has more than $\frac{2}{5}\sqrt{5}^γ$ minimum dominating sets. Furthermore, we disprove a conjecture about the number of minimum total dominating sets in forests by Henning, Mohr and Rautenbach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_13182 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the number of minimum dominating sets and total dominating sets in forests Petr, Jan Portier, Julien Versteegen, Leo Combinatorics We show that the maximum number of minimum dominating sets of a forest with domination number $γ$ is at most $\sqrt{5}^γ$ and construct for each $γ$ a tree with domination number $γ$ that has more than $\frac{2}{5}\sqrt{5}^γ$ minimum dominating sets. Furthermore, we disprove a conjecture about the number of minimum total dominating sets in forests by Henning, Mohr and Rautenbach. |
| title | On the number of minimum dominating sets and total dominating sets in forests |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2206.13182 |