# Get the next minimal color from direct parents
	private fun min_color(e: E): Int do
		var max_color = -1
		for p in poset_cache[e].direct_greaters do
			if not colors_cache.has_key(p) then continue
			var color = colors_cache[p]
			if color > max_color then max_color = color
		end
		return max_color + 1
	end