Geodesic
A note on long cycles in sparse random graphs
The electronic journal of combinatorics, Tome 30 (2023) no. 2
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

Let $L_{c,n}$ denote the size of the longest cycle in $G(n,{c}/{n})$, $c>1$ constant. We show that there exists a continuous function $f(c)$ such that $ L_{c,n}/n \to f(c)$ a.s. for $c\geq 20$, thus extending a result of Frieze and the author to smaller values of $c$. Thereafter, for $c\geq 20$, we determine the limit of the probability that $G(n,c/n)$ contains cycles of every length between the length of its shortest and its longest cycles as $n\to \infty$.
DOI : 10.37236/11471
Classification : 05C80, 05C38, 05C12
Mots-clés : weakly pancyclic graphs, longest cycle, sparse random graph, scaling limit

Michael Anastos  1

1 ISTA 
@article{10_37236_11471,
     author = {Michael Anastos},
     title = {A note on long cycles in sparse random graphs},
     journal = {The electronic journal of combinatorics},
     year = {2023},
     volume = {30},
     number = {2},
     doi = {10.37236/11471},
     zbl = {1514.05140},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/11471/}
}
TY  - JOUR
AU  - Michael Anastos
TI  - A note on long cycles in sparse random graphs
JO  - The electronic journal of combinatorics
PY  - 2023
VL  - 30
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.37236/11471/
DO  - 10.37236/11471
ID  - 10_37236_11471
ER  - 
%0 Journal Article
%A Michael Anastos
%T A note on long cycles in sparse random graphs
%J The electronic journal of combinatorics
%D 2023
%V 30
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/11471/
%R 10.37236/11471
%F 10_37236_11471
Michael Anastos. A note on long cycles in sparse random graphs. The electronic journal of combinatorics, Tome 30 (2023) no. 2. doi: 10.37236/11471

Cité par Sources :