(* Knuderne er sorteret i stigende order *)
fun select [] n used = []
  | select ((v,[])::st) (n::ns) used = (v,n)::(select st (n::ns) ((v,n)::used))
  | select ((v,l)::st) n used =
  let
    fun checkNeighbour [] used = []
    fun checkNeighbour l [] = []
      | checkNeighbour (lv::l) ((uv,un)::used) =
      if (lv = uv) then
      un::(checkNeighbour l used)
      else (checkNeighbour l ((uv,un)::used))@(checkNeighbour (lv::l) used)
    val usedReg = checkNeighbour l used
    fun checkReg [] ur = 0
      | checkReg n [] = 0
      | checkReg (n::ns) ur = (if (List.exists k ur2) then
                   checkReg ns ur
                   else n)
    val aReg = checkReg n usedReg
  in
      (v,aReg)::(select st n ((v,aReg)::used))
  end

fun simplify [] E n st = select st n
  | simplify (v::V) E n st =
  let
    fun removeEdges v [] E2 = E2
      | removeEdges v ((s,t)::E) E2 =
      if (v = s) || (v = t) then
      removeEdges v E E2
      else removeEdges v E e::E2
    fun neighbours v [] l = l
      | neighbours v ((s,t)::E) l =
    case (s,t) of
      (v,t) => neighbours v E (t::l)
              | (s,v) => neighbours v E (s::l)
    val edges = removeEdges v E []
    val l = neighbours v E []
  in
      simplify V edges n (v,l)::st
  end