Geodesic
Turán density of 2-edge-colored bipartite graphs with application on \(\{2, 3\}\)-hypergraphs
Shuliang Bai ; Linyuan Lu1
1University of South Carolina
The electronic journal of combinatorics, Tome 28 (2021) no. 3
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

We consider the Turán problems of $2$-edge-colored graphs. A $2$-edge-colored graph $H=(V, E_r, E_b)$ is a triple consisting of the vertex set $V$, the set of red edges $E_r$ and the set of blue edges $E_b$ where $E_r$ and $E_b$ do not have to be disjoint. The Turán density $\pi(H)$ of $H$ is defined to be $\lim_{n\to\infty} \max_{G_n}h_n(G_n)$, where $G_n$ is chosen among all possible $2$-edge-colored graphs on $n$ vertices containing no $H$ as a sub-graph and $h_n(G_n)=(|E_r(G)|+|E_b(G)|)/\binom{n}{2}$ is the formula to measure the edge density of $G_n$. We will determine the Turán densities of all $2$-edge-colored bipartite graphs. We also give an important application on the Turán problems of $\{2, 3\}$-hypergraphs.
DOI : 10.37236/10068
Classification : 05C30, 05C15, 05C65, 05D40, 05C35
Mots-clés : hypergraph Turán problem, extremal set theory

Shuliang Bai    ; Linyuan Lu  1

1 University of South Carolina 
@article{10_37236_10068,
     author = {Shuliang Bai and Linyuan  Lu},
     title = {Tur\'an density of 2-edge-colored bipartite graphs with application on \(\{2, 3\}\)-hypergraphs},
     journal = {The electronic journal of combinatorics},
     year = {2021},
     volume = {28},
     number = {3},
     doi = {10.37236/10068},
     zbl = {1471.05044},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/10068/}
}
TY  - JOUR
AU  - Shuliang Bai
AU  - Linyuan  Lu
TI  - Turán density of 2-edge-colored bipartite graphs with application on \(\{2, 3\}\)-hypergraphs
JO  - The electronic journal of combinatorics
PY  - 2021
VL  - 28
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.37236/10068/
DO  - 10.37236/10068
ID  - 10_37236_10068
ER  - 
%0 Journal Article
%A Shuliang Bai
%A Linyuan  Lu
%T Turán density of 2-edge-colored bipartite graphs with application on \(\{2, 3\}\)-hypergraphs
%J The electronic journal of combinatorics
%D 2021
%V 28
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/10068/
%R 10.37236/10068
%F 10_37236_10068
Shuliang Bai; Linyuan  Lu. Turán density of 2-edge-colored bipartite graphs with application on \(\{2, 3\}\)-hypergraphs. The electronic journal of combinatorics, Tome 28 (2021) no. 3. doi: 10.37236/10068

Cité par Sources :