Geodesic
Paths, cycles and sprinkling in random hypergraphs
Oliver Cooley1
1Graz University of Technology
The electronic journal of combinatorics, Tome 32 (2025) no. 3
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

We prove a lower bound on the length of the longest $j$-tight cycle in a $k$-uniform binomial random hypergraph for any $2 \le j \le k-1$. We first prove the existence of a $j$-tight path of the required length. The standard "sprinkling" argument is not enough to show that this path can be closed to a $j$-tight cycle - we therefore show that the path has many extensions, which is sufficient to allow the sprinkling to close the cycle.
DOI : 10.37236/10354
Classification : 05C80, 05C65, 05C38
Mots-clés : random graph, hypergraph, path, cycle

Oliver Cooley  1

1 Graz University of Technology 
@article{10_37236_10354,
     author = {Oliver Cooley},
     title = {Paths, cycles and sprinkling in random hypergraphs},
     journal = {The electronic journal of combinatorics},
     year = {2025},
     volume = {32},
     number = {3},
     doi = {10.37236/10354},
     zbl = {8097657},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/10354/}
}
TY  - JOUR
AU  - Oliver Cooley
TI  - Paths, cycles and sprinkling in random hypergraphs
JO  - The electronic journal of combinatorics
PY  - 2025
VL  - 32
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.37236/10354/
DO  - 10.37236/10354
ID  - 10_37236_10354
ER  - 
%0 Journal Article
%A Oliver Cooley
%T Paths, cycles and sprinkling in random hypergraphs
%J The electronic journal of combinatorics
%D 2025
%V 32
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/10354/
%R 10.37236/10354
%F 10_37236_10354
Oliver Cooley. Paths, cycles and sprinkling in random hypergraphs. The electronic journal of combinatorics, Tome 32 (2025) no. 3. doi: 10.37236/10354

Cité par Sources :