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Link to paper, as requested (and delete "= 18", which isn't part of the title)
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LSpice
LSpice
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I'm studying the Ramsey numbers, especially $R(3,6) = 18$

I understand that the proof using the theorem $R(m,n) <R(m-1,n)+R(m,n-1)$ can only prove that $R(3,6)<20$. However by Cariolaro's "On the Ramsey number $R(3,6) = 18$"On the Ramsey number $R(3,6)$" I understand the proof for $R(3,6)<19$.

Now I try to understand the proof for $R(3,6)>17$, but the graph there is built with some program. I read that it is possible to build a graph to test $R(3,6)>17$ without programs.

In "thesis (Ph. D.)--University of Waterloo, 1966, Chromatic Graphs and Ramsey's Theorem"Chromatic Graphs and Ramsey's Theorem" by J. G. Kalbfleisch this result supposedly exists, but unfortunately I can not find the document. Can someone give the idea of ​​the construction or do you know of any document or article where you do it?

I'm studying the Ramsey numbers, especially $R(3,6) = 18$

I understand that the proof using the theorem $R(m,n) <R(m-1,n)+R(m,n-1)$ can only prove that $R(3,6)<20$. However by Cariolaro's "On the Ramsey number $R(3,6) = 18$" I understand the proof for $R(3,6)<19$.

Now I try to understand the proof for $R(3,6)>17$, but the graph there is built with some program. I read that it is possible to build a graph to test $R(3,6)>17$ without programs.

In "thesis (Ph. D.)--University of Waterloo, 1966, Chromatic Graphs and Ramsey's Theorem" by J. G. Kalbfleisch this result supposedly exists, but unfortunately I can not find the document. Can someone give the idea of ​​the construction or do you know of any document or article where you do it?

I'm studying the Ramsey numbers, especially $R(3,6) = 18$

I understand that the proof using the theorem $R(m,n) <R(m-1,n)+R(m,n-1)$ can only prove that $R(3,6)<20$. However by Cariolaro's "On the Ramsey number $R(3,6)$" I understand the proof for $R(3,6)<19$.

Now I try to understand the proof for $R(3,6)>17$, but the graph there is built with some program. I read that it is possible to build a graph to test $R(3,6)>17$ without programs.

In "thesis (Ph. D.)--University of Waterloo, 1966, Chromatic Graphs and Ramsey's Theorem" by J. G. Kalbfleisch this result supposedly exists, but unfortunately I can not find the document. Can someone give the idea of ​​the construction or do you know of any document or article where you do it?

This is a reference request + English
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edit approved Oct 7, 2018 at 22:20
Amir Sagiv
edit approved Oct 7, 2018 at 22:20
Amir Sagiv
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$R(3,6) = 18$, especially proving that $R(3,6)>17$

I'm studying the ramseyRamsey numbers, especially $R(3,6) = 18$

I understand that the proof withusing the theorem $R(m,n) <R(m-1,n)+R(m,n-1)$ iscan only possible to prove that $R(3,6)<20$, however. However by Cariolaro's "On the ramseyRamsey number $R(3,6) = 18$ of Cariolaro"" I understand the demonstrationproof for $R(3,6)<19$.

Now I try to understand the demonstrationproof for $R(3,6)>17$, but the graph there is built with some program,. I read that if it is possible to build a graph to test $R(3,6)>17$ without programs, in.

In "thesis (Ph. D.)--University of Waterloo, 1966, Chromatic Graphs and Ramsey's Theorem ofTheorem" by J. G. Kalbfleisch" he does itKalbfleisch this result supposedly exists, but unfortunately I can not find the document, someone. Can yousomeone give the idea of ​​construction​​the construction or do you know of any document or article where you do it?

$R(3,6) = 18$, especially $R(3,6)>17$

I'm studying the ramsey numbers, especially $R(3,6) = 18$

I understand that the proof with the theorem $R(m,n) <R(m-1,n)+R(m,n-1)$ is only possible to prove that $R(3,6)<20$, however by "On the ramsey number $R(3,6) = 18$ of Cariolaro" I understand the demonstration for $R(3,6)<19$.

Now I try to understand the demonstration for $R(3,6)>17$, but the graph is built with some program, I read that if it is possible to build a graph to test $R(3,6)>17$ without programs, in "thesis (Ph. D.)--University of Waterloo, 1966, Chromatic Graphs and Ramsey's Theorem of J. G. Kalbfleisch" he does it, but unfortunately I can not find the document, someone Can you give the idea of ​​construction or do you know of any document or article where you do it?

$R(3,6) = 18$, especially proving that $R(3,6)>17$

I'm studying the Ramsey numbers, especially $R(3,6) = 18$

I understand that the proof using the theorem $R(m,n) <R(m-1,n)+R(m,n-1)$ can only prove that $R(3,6)<20$. However by Cariolaro's "On the Ramsey number $R(3,6) = 18$" I understand the proof for $R(3,6)<19$.

Now I try to understand the proof for $R(3,6)>17$, but the graph there is built with some program. I read that it is possible to build a graph to test $R(3,6)>17$ without programs.

In "thesis (Ph. D.)--University of Waterloo, 1966, Chromatic Graphs and Ramsey's Theorem" by J. G. Kalbfleisch this result supposedly exists, but unfortunately I can not find the document. Can someone give the idea of ​​the construction or do you know of any document or article where you do it?

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Janeth Benavides
Janeth Benavides
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$R(3,6) = 18$, especially $R(3,6)>17$

I'm studying the ramsey numbers, especially $R(3,6) = 18$

I understand that the proof with the theorem $R(m,n) <R(m-1,n)+R(m,n-1)$ is only possible to prove that $R(3,6)<20$, however by "On the ramsey number $R(3,6) = 18$ of Cariolaro" I understand the demonstration for $R(3,6)<19$.

Now I try to understand the demonstration for $R(3,6)>17$, but the graph is built with some program, I read that if it is possible to build a graph to test $R(3,6)>17$ without programs, in "thesis (Ph. D.)--University of Waterloo, 1966, Chromatic Graphs and Ramsey's Theorem of J. G. Kalbfleisch" he does it, but unfortunately I can not find the document, someone Can you give the idea of ​​construction or do you know of any document or article where you do it?