This is the output of running the program E6.
There are 390 edges in the graph and 144 maximal independent sets.
The request for an 8-coloring fails and the request for a 9-coloring returns 
the coloring below.  The numbers refer to the positive roots in the order
they are given by the function pos_roots.

                                    R := E6

                                      390

                                      144

                              false, c, 67.883130

true,

   [{1, 7, 12, 18, 23}, {6, 11, 20, 25, 27}, {3, 9, 13, 29, 32},

       {5, 10, 14, 31, 33}, {4, 16, 28, 30, 35}, {8, 17, 26, 36}, {2, 19, 22},

       {15, 21, 34}, {24}],

   .087960

bytes used=857955116, alloc=1703624, time=92.93