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:
  1. All two-colourings of k-regular graphs (k=3,4,5)
  2. All three-colourings of k-regular graphs (k=3,4,5)
  3. All four-colourings of k-regular graphs (k=3,4,5)
• Sage data files:
  1. Lists for two colours, the lists l23, l24, l25 contain all parameter matrices for 3-regular, respectively 4-regular, respectively 5-regular graphs.
  2. Lists for three colours, the lists l33, l34, l35 contain all parameter matrices for 3-regular, respectively 4-regular, respectively 5-regular graphs.
  3. 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.