2
votes
1answer
181 views

Coloring of subgraphs of G^n

Let $G=(L,R,E)$ be a finite bipartite graph, such that for each $v\in L\cup R: deg(v)>0$. Define $E^{(n)}=\{(\overline{l},\overline{r}) | \overline{l}=(l_1,...,l_n)\in L^n , ...
4
votes
2answers
122 views

Is There a Graph that is Ramsey for $P_{2n}$ but is $C_{2n+1}-$free

Write $F\to G$ to mean that for every two coloring of the edges of $F$, there exists a monochromatic copy of $G$. Nesetril and Rodl proved that for a graph $G$, there exists a graph $F\to G$ with ...
2
votes
1answer
173 views

A Ramsey-like lower bound?

Does there exist a graph $G$ which cannot be properly vertex-coloured with 3 colours (i.e. $G$ has chromatic number at least 4), such that for every graph $H$, if $H$ contains a triangle but there ...
5
votes
2answers
465 views

The Problem about 2-coloring finite plane

Suppose we color a $X \times X$ finite plane by red and blue arbitrarily. How large does X need to be to guarantee a monochromatic combinatorial square $k \times k$ 1 0 1 0 1 1 1 1 1 1 1 1 1 ...
3
votes
2answers
506 views

Where can I find a catalog of known Ramsey numbers?

Is there an online catalog available of Ramsey numbers, preferably one that for unknown values documents the known upper/lower bounds?
8
votes
5answers
946 views

Can one make Erdős's Ramsey lower bound explicit?

Erdős's 1947 probabilistic trick provided a lower exponential bound for the Ramsey number R(k). Is it possible to explicitly construct 2-colourings on exponentially sized graphs without large ...