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5
votes
1answer
191 views
Known bounds and values for Ramsey Numbers
Is there a good online reference that lists known bounds on Ramsey numbers (and is relatively up to date)? The wikipedia page only has numbers for $R_2(n,m)$.
I am specifically interested in known ...
6
votes
1answer
154 views
Any partition of $\{1,2,\ldots,9\}$ must contain a $3$-Term Arithmetic Progression
Prove that for any way of dividing the set $X=\{1,2,3,\dots,9\}$ into $2$ sets, there always exist at least one arithmetic progression of length $3$ in one of the two sets.
3
votes
1answer
98 views
Permutation of 1…9 with no ascending or descending subsequence of length 4
Arrange the numbers $1,2,...,9$ in such an order that no four of them appear (adjacently or otherwise) in ascending or descending order.
Show that there is no arrangement of the numbers $1,2,...,10$ ...
3
votes
1answer
88 views
Amalgamation of graphs
I am trying to understand the definition of amalgamation of a $n+1$-partite graph as explained here(first few lines of page 4). We have a $n+1$-partite graph $G$ with partite sets $V_0,V_1,\cdots,V_n$ ...
3
votes
2answers
68 views
Counterexample for $R(4,4) \neq 8$
I try to find a counterexample for $R(4,4)\neq 8$. (R is the Ramsey-number).
I drew a graph with 8 vedges and I coloured all edges $(v_i,v_j)$ with $i-j =\pm 2,4,6$ in the same colour (for example ...
2
votes
1answer
94 views
Ramsey Number proof
I am trying to prove:
$R(3,3,3,3)\leq 4(R(3,3,3)-1) + 2$
I am confused as to how one can go from a $4$ color problem to a $3$ color problem by multiplying and adding.
edit: $R$ is the Ramsey ...
1
vote
1answer
79 views
Best known bounds for Ramsey numbers
I realize a similar question has been asked before but what I want to know is a little different and is not answered by the link in the answer to that question. I am interested in knowing the best ...
