#!/usr/local/bin/ruby

class Graph
  attr :vertices
  attr :edges

  def initialize(vertices = [], edges = Hash.new {|h, k| h[k] = Hash.new {0} })
    @vertices = vertices
    @edges = edges
  end
end

def grow(graph, a, b)
  vertices = graph.vertices.dup
  edges = graph.edges.dup
  c = vertices.size

  vertices << c

  edges[a][c] += 1
  edges[c][b] += 1

  Graph.new(vertices, edges)
end

game = [Graph.new([0, 1])]
p game.map {|g| g.vertices.combination(2).to_a }