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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 $R(3,6)$" 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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    $\begingroup$ Perhaps math.stackexchange.com/questions/3333/… will answer your question. $\endgroup$
    – Gerry Myerson
    Commented Oct 7, 2018 at 22:40
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    $\begingroup$ The thesis can be searched here: hdl.handle.net/2027/mdp.39015014352580 but without logging in one cannot see even snippet results (and even if you log in, I don't know what you'll get). Other than that, ask for an inter-library loan, if it is possible. $\endgroup$
    – David Roberts ♦
    Commented Oct 8, 2018 at 1:48
  • $\begingroup$ the thesis has been digitized by HathiTrust but only limited search is available because of copyright restrictions. I presume this means there is no (legal) online copy and borrowing a print version is the only option. $\endgroup$
    – Carlo Beenakker
    Commented Oct 8, 2018 at 6:10

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