Additional material to "Perfect colourings of regular graphs"
In "Perfect colourings of regular graphs" Joseph Damasco and me
determined all parameter matrices that correspond to perfect colourings
of k-regular connected graphs for k in {3,4,5}. The entire
list
is pretty long. Hence part of the list is omitted from the paper
and the complete list is available here.
The sage worksheets are available here, too. Some of them need several
hours of computation. So the already computed lists are also
available here as sage data files.
- All possible parameter matrices
for k-regular graphs
for k in {3,4,5} with two, three or for colours
- Sage worksheets:
- All two-colourings of
k-regular graphs (k=3,4,5)
- All three-colourings of
k-regular graphs (k=3,4,5)
- All four-colourings of
k-regular graphs (k=3,4,5)
- Sage data files:
- Lists for two colours, the lists
l23, l24, l25 contain all parameter matrices for 3-regular,
respectively 4-regular, respectively 5-regular graphs.
- Lists for three colours, the lists
l33, l34, l35 contain all parameter matrices for 3-regular,
respectively 4-regular, respectively 5-regular graphs.
- Lists for four colours, the lists
l43, l44, l45 contain all parameter matrices for 3-regular,
respectively 4-regular, respectively 5-regular graphs.
The sage data files can be loaded into any sage worksheet:
open('path/to/file/4col-list.sage')
The sage worksheets can be just opened with sage. Then
each cell needs to be executed with SHIFT-RETURN.
Dirk Frettlöh, 26th February 2018