multicolor ramsey number
Recently Published Documents


TOTAL DOCUMENTS

7
(FIVE YEARS 0)

H-INDEX

2
(FIVE YEARS 0)

2019 ◽  
Vol 342 (1) ◽  
pp. 217-220 ◽  
Author(s):  
Qizhong Lin ◽  
Weiji Chen

10.37236/6670 ◽  
2017 ◽  
Vol 24 (1) ◽  
Author(s):  
Tomasz Łuczak ◽  
Joanna Polcyn

We show that if we color the hyperedges of the complete $3$-uniform hypergraph on $2n+\sqrt{18n+1}+2$ vertices with $n$ colors, then one of the color classes contains a loose path of length three.


2016 ◽  
Vol 339 (12) ◽  
pp. 2857-2860 ◽  
Author(s):  
Kathleen Johst ◽  
Yury Person

2016 ◽  
Vol 59 (01) ◽  
pp. 190-196 ◽  
Author(s):  
Ghaffar Raeisi ◽  
Ali Zaghian

Abstract Let G 1, G 2 , …, Gt be arbitrary graphs. The Ramsey number R(G 1 , G 2, …, Gt ) is the smallest positive integer n such that if the edges of the complete graph Kn are partitioned into t disjoint color classes giving t graphs H 1, H 2, …, H t, then at least one Hi has a subgraph isomorphic to Gi. In this paper, we provide the exact value of the R(Tn, Wm) for odd m, n ≥ m−1, where T n is either a caterpillar, a tree with diameter at most four, or a tree with a vertex adjacent to at least leaves, and W n is the wheel on n + 1 vertices. Also, we determine R(C n, W m) for even integers n and m, n ≥ m + 500, which improves a result of Shi and confirms a conjecture of Surahmat et al. In addition, the multicolor Ramsey number of trees versus an odd wheel is discussed in this paper.


10.37236/511 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Gholam Reza Omidi ◽  
Ghaffar Raeisi

Let $G_1, G_2, G_3, \ldots , G_t$ be graphs. The multicolor Ramsey number $R(G_1, G_2, \ldots, G_t)$ is the smallest positive integer $n$ such that if the edges of a complete graph $K_n$ are partitioned into $t$ disjoint color classes giving $t$ graphs $H_1,H_2,\ldots,H_t$, then at least one $H_i$ has a subgraph isomorphic to $G_i$. In this paper, we provide the exact value of $R(P_{n_1}, P_{n_2},\ldots, P_{n_t},C_k)$ for certain values of $n_i$ and $k$. In addition, the exact values of $R(P_5,C_4,P_k)$, $R(P_4,C_4,P_k)$, $R(P_5,P_5,P_k)$ and $R(P_5,P_6,P_k)$ are given. Finally, we give a lower bound for $R(P_{2n_1}, P_{2n_2},\ldots, P_{2n_t})$ and we conjecture that this lower bound is the exact value of this number. Moreover, some evidence is given for this conjecture.


10.37236/1081 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Tomasz Dzido ◽  
Marek Kubale ◽  
Konrad Piwakowski

For given graphs $G_{1}, G_{2}, ... , G_{k}$, where $k \geq 2$, the multicolor Ramsey number $R(G_{1}, G_{2}, ... , G_{k})$ is the smallest integer $n$ such that if we arbitrarily color the edges of the complete graph on $n$ vertices with $k$ colors, there is always a monochromatic copy of $G_{i}$ colored with $i$, for some $1 \leq i \leq k$. Let $P_k$ (resp. $C_k$) be the path (resp. cycle) on $k$ vertices. In the paper we show that $R(P_3,C_k,C_k)=R(C_k,C_k)=2k-1$ for odd $k$. In addition, we provide the exact values for Ramsey numbers $R(P_{4}, P_{4}, C_{k})=k+2$ and $R(P_{3}, P_{5}, C_{k})=k+1$.


10.37236/1980 ◽  
2005 ◽  
Vol 12 (1) ◽  
Author(s):  
Tomasz Dzido ◽  
Andrzej Nowik ◽  
Piotr Szuca

For given finite family of graphs $G_{1}, G_{2}, \ldots , G_{k}, k \geq 2$, the multicolor Ramsey number $R(G_{1}, G_{2}, \ldots , G_{k})$ is the smallest integer $n$ such that if we arbitrarily color the edges of the complete graph on $n$ vertices with $k$ colors then there is always a monochromatic copy of $G_{i}$ colored with $i$, for some $1 \leq i \leq k$. We give a lower bound for $k-$color Ramsey number $R(C_{m}, C_{m}, \ldots , C_{m})$, where $m \geq 4$ is even and $C_{m}$ is the cycle on $m$ vertices.


Sign in / Sign up

Export Citation Format

Share Document