Bounds on the lettericity of graphs
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916455506771968 |
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| author | Mandrick, Sean Vatter, Vincent |
| author_facet | Mandrick, Sean Vatter, Vincent |
| contents | Lettericity measures the minimum size of an alphabet needed to represent a graph as a letter graph, where vertices are encoded by letters, and edges are determined by an underlying decoder. We prove that all graphs on~$n$ vertices have lettericity at most approximately $n - \tfrac{1}{2} \log_2 n$ and that almost all graphs on $n$ vertices have lettericity at least $n - (2 \log_2 n + 2 \log_2 \log_2 n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_02920 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bounds on the lettericity of graphs Mandrick, Sean Vatter, Vincent Combinatorics Lettericity measures the minimum size of an alphabet needed to represent a graph as a letter graph, where vertices are encoded by letters, and edges are determined by an underlying decoder. We prove that all graphs on~$n$ vertices have lettericity at most approximately $n - \tfrac{1}{2} \log_2 n$ and that almost all graphs on $n$ vertices have lettericity at least $n - (2 \log_2 n + 2 \log_2 \log_2 n)$. |
| title | Bounds on the lettericity of graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2305.02920 |