anneal=: {{
  best=. i.#y [ cost=. #~.greedy y
  for.i.#y do.
    o=. ?~#y
    c=.#~.greedy o ([ { {"1) y
    if. cost > c do.
      best=. o [ cost=. c
    end.
  end.
  (/:best) { greedy best ([ { {"1) y
}}
task=: {{
  colors=. anneal parse y
  echo'nodes: %d, edges: %d, colours: %d' sprintf #each graph;ref;~.colors
  edgecolors=. <@(,&":':',&":])/"1(>labels i.L:1 ref){colors
  ,./>' ',.~each^:2(cut y),:each edgecolors
}}

   task ex1
nodes: 4, edges: 4, colours: 3
0-1  1-2  2-0  3
0:1  1:2  2:0  0:0

   task ex2
nodes: 8, edges: 12, colours: 2
1-6  1-7  1-8  2-5  2-7  2-8  3-5  3-6  3-8  4-5  4-6  4-7
0:1  0:1  0:1  0:1  0:1  0:1  0:1  0:1  0:1  0:1  0:1  0:1

   task ex3
nodes: 8, edges: 12, colours: 2
1-4  1-6  1-8  3-2  3-6  3-8  5-2  5-4  5-8  7-2  7-4  7-6
0:1  0:1  0:1  0:1  0:1  0:1  0:1  0:1  0:1  0:1  0:1  0:1

   task ex4
nodes: 8, edges: 12, colours: 2
1-6  7-1  8-1  5-2  2-7  2-8  3-5  6-3  3-8  4-5  4-6  4-7
0:1  1:0  1:0  1:0  0:1  0:1  0:1  1:0  0:1  0:1  0:1  0:1