1. A graph is dismantlable if and only if it has a dismantling order.
  2. By induction, it follows that every cop-win graph is dismantlable.
  3. They are also dismantlable for cleaning or repair.
  4. It is arguable that this is artificial economics, based on the cultural preference for wastefulness and that Zero Waste designs of dismantlable components will ultimately be the cheapest as well as the most conservative way to reuse buildings.
  5. In an arbitrary graph that is not cop-win, the robber can win by removing all dominated vertices and playing within the remaining subgraph, which must be non-empty else the graph would be dismantlable.


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