On the hat guessing number of a planar graph class
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866911179682611200 |
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| author | Bradshaw, Peter |
| author_facet | Bradshaw, Peter |
| contents | The hat guessing number is a graph invariant based on a hat guessing game introduced by Winkler. Using a new vertex decomposition argument involving an edge density theorem of Erdős for hypergraphs, we show that the hat guessing number of all outerplanar graphs is less than $2^{125000}$. We also define the class of layered planar graphs, which contains outerplanar graphs, and we show that every layered planar graph has bounded hat guessing number. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_01480 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the hat guessing number of a planar graph class Bradshaw, Peter Combinatorics 05C15, 05C57 The hat guessing number is a graph invariant based on a hat guessing game introduced by Winkler. Using a new vertex decomposition argument involving an edge density theorem of Erdős for hypergraphs, we show that the hat guessing number of all outerplanar graphs is less than $2^{125000}$. We also define the class of layered planar graphs, which contains outerplanar graphs, and we show that every layered planar graph has bounded hat guessing number. |
| title | On the hat guessing number of a planar graph class |
| topic | Combinatorics 05C15, 05C57 |
| url | https://arxiv.org/abs/2106.01480 |