The Gamma-Theta Conjecture holds for planar graphs
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913915868282880 |
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| author | Taletskii, Dmitrii |
| author_facet | Taletskii, Dmitrii |
| contents | The Gamma-Theta Conjecture states that if the domination number of a graph is equal to its eternal domination number, then it is also equal to its clique covering number. This conjecture is known to be true for several graph classes, such as outerplanar graphs, subcubic graphs and $C_k$-free graphs, where $k \in \{3,4\}$. In this paper, we prove the Conjecture for the class of planar graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20120 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Gamma-Theta Conjecture holds for planar graphs Taletskii, Dmitrii Combinatorics 05C69 The Gamma-Theta Conjecture states that if the domination number of a graph is equal to its eternal domination number, then it is also equal to its clique covering number. This conjecture is known to be true for several graph classes, such as outerplanar graphs, subcubic graphs and $C_k$-free graphs, where $k \in \{3,4\}$. In this paper, we prove the Conjecture for the class of planar graphs. |
| title | The Gamma-Theta Conjecture holds for planar graphs |
| topic | Combinatorics 05C69 |
| url | https://arxiv.org/abs/2412.20120 |