  This paper sets out the results of a range of searches for linear and cyclic
graph colourings with specific Ramsey properties. The new graphs comprise
mainly 'template graphs' which can be used in a construction described by the
current author in 2021 to build linear or cyclic compound graphs with inherited
Ramsey properties. These graphs result in improved lower bounds for a wide
range of multicolour Ramsey numbers.
  Searches were carried out using relatively simple programs (written in the
language `C') to generate clauses for input to the PeneLoPe and Plingeling
parallel SAT-solvers. When solutions were found, the output from the solvers
specified the desired graph colourings.
  The majority of the graphs produced by this work are `template graphs' with
parameters in the form $(k,k,3)$ or $(k,l,3)$ with $k \ne l$. Using these
template graphs in familiar constructions, it has been possible to demonstrate
significant improvements for lower bounds for most $R_r(k)$ for $5 \le k \le 9$
and $r \ge 4$. These improvements provide correspondingly increased lower
bounds on $\Gamma(k) = \lim_{\substack{r \rightarrow \infty}} R{_r}(k)^{1/r}$.
  We also show that $R_3(8) \ge 7174$ and $R_3(9) \ge 15041$. Other new lower
bounds include $R(3,6,6) \ge 338$ and $R(3,8,8) \ge 941$, based on non-template
cyclic graphs, and the interesting particular cases $R(3,4,5,5) \ge 729$ and
$R(3,5,5,5) \ge 1429$.
  A spreadsheet containing specimens of many of the graphs mentioned here will
be attached as an ArXiv ancillary file.
