Geodesic
Generalized Ramsey numbers for graphs with three disjoint cycles versus a complete graph
Shinya Fujita1
1Maebashi Institute of Technology
The electronic journal of combinatorics, Tome 19 (2012) no. 2
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

Let $\mathcal{F},\mathcal{G}$ be families of graphs. The generalized Ramsey number $r(\mathcal{F},\mathcal{G})$ denotes the smallest value of $n$ for which every red-blue coloring of $K_n$ yields a red $F\in\mathcal{F}$ or a blue $G\in \mathcal{G}$. Let $\mathcal{F}(k)$ be a family of graphs with $k$ vertex-disjoint cycles.In this paper, we deal with the case where $\mathcal{F}=\mathcal{F}(3),\mathcal{G}=\{K_t\}$ for some fixed $t$ with $t\ge 2$, and prove that $r(\mathcal{F}(3),\mathcal{G})=2t+5$.
DOI : 10.37236/2268
Classification : 05C55, 05C15, 05C35, 05C75
Mots-clés : independence number, Ramsey number, vertex-disjoint cycles

Shinya Fujita  1

1 Maebashi Institute of Technology 
@article{10_37236_2268,
     author = {Shinya Fujita},
     title = {Generalized {Ramsey} numbers for graphs with three disjoint cycles versus a complete graph},
     journal = {The electronic journal of combinatorics},
     year = {2012},
     volume = {19},
     number = {2},
     doi = {10.37236/2268},
     zbl = {1243.05160},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2268/}
}
TY  - JOUR
AU  - Shinya Fujita
TI  - Generalized Ramsey numbers for graphs with three disjoint cycles versus a complete graph
JO  - The electronic journal of combinatorics
PY  - 2012
VL  - 19
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.37236/2268/
DO  - 10.37236/2268
ID  - 10_37236_2268
ER  - 
%0 Journal Article
%A Shinya Fujita
%T Generalized Ramsey numbers for graphs with three disjoint cycles versus a complete graph
%J The electronic journal of combinatorics
%D 2012
%V 19
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/2268/
%R 10.37236/2268
%F 10_37236_2268
Shinya Fujita. Generalized Ramsey numbers for graphs with three disjoint cycles versus a complete graph. The electronic journal of combinatorics, Tome 19 (2012) no. 2. doi: 10.37236/2268

Cité par Sources :