Bounds on the Lettericity of Graphs

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 $n - \tfrac{1}{2} \log_2 n$ an...

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Bibliographic Details
Published inThe Electronic journal of combinatorics Vol. 31; no. 4
Main Authors Mandrick, Sean, Vatter, Vincent
Format Journal Article
LanguageEnglish
Published 29.11.2024
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Summary: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 $n - (2 \log_2 n + 2 \log_2 \log_2 n)$.
ISSN:1077-8926
1077-8926
DOI:10.37236/12411