We analyze a random greedy process to construct $q$-uniform linear hypergraphs using the differential equation method. We show for $q=o(\sqrt{\log n})$, that this process yields a hypergraph with $\frac{n(n-1)}{q(q-1)}(1-o(1))$ edges. We also give some bounds for maximal linear hypergraphs.
@article{10_37236_12303,
author = {Sayok Chakravarty and Nicholas Spanier},
title = {The linear \(q\)-hypergraph process},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {1},
doi = {10.37236/12303},
zbl = {1559.05132},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12303/}
}
TY - JOUR
AU - Sayok Chakravarty
AU - Nicholas Spanier
TI - The linear \(q\)-hypergraph process
JO - The electronic journal of combinatorics
PY - 2025
VL - 32
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/12303/
DO - 10.37236/12303
ID - 10_37236_12303
ER -
%0 Journal Article
%A Sayok Chakravarty
%A Nicholas Spanier
%T The linear \(q\)-hypergraph process
%J The electronic journal of combinatorics
%D 2025
%V 32
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/12303/
%R 10.37236/12303
%F 10_37236_12303
Sayok Chakravarty; Nicholas Spanier. The linear \(q\)-hypergraph process. The electronic journal of combinatorics, Tome 32 (2025) no. 1. doi: 10.37236/12303
