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 $n - (2 \log_2 n + 2 \log_2 \log_2 n)$.
@article{10_37236_12411,
author = {Sean Mandrick and Vincent Vatter},
title = {Bounds on the lettericity of graphs},
journal = {The electronic journal of combinatorics},
year = {2024},
volume = {31},
number = {4},
doi = {10.37236/12411},
zbl = {1556.05076},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12411/}
}
TY - JOUR
AU - Sean Mandrick
AU - Vincent Vatter
TI - Bounds on the lettericity of graphs
JO - The electronic journal of combinatorics
PY - 2024
VL - 31
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/12411/
DO - 10.37236/12411
ID - 10_37236_12411
ER -
%0 Journal Article
%A Sean Mandrick
%A Vincent Vatter
%T Bounds on the lettericity of graphs
%J The electronic journal of combinatorics
%D 2024
%V 31
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/12411/
%R 10.37236/12411
%F 10_37236_12411
Sean Mandrick; Vincent Vatter. Bounds on the lettericity of graphs. The electronic journal of combinatorics, Tome 31 (2024) no. 4. doi: 10.37236/12411
