Constructible graphs and pursuit

A (finite or infinite) graph is called constructible if it may be obtained recursively from the one-point by repeatedly adding dominated vertices. In finite case, graphs are precisely cop-win graphs, but for infinite situation not well understood. One of our aims in this paper to give a that constructible. This first known such example. We also show every countable ordinal arises as rank some graph, answering question Evron, Solomon and Stahl. addition, we which there no construction order whose associated domination map homomorphism, Chastand, Laviolette Polat. Lehner showed weak cop win (meaning can eventually force robber out any set). Our other main aim investigate how notion relates ‘locally constructible’ (every contained subgraph). that, under mild extra conditions, locally win. But an example general, need Surprisingly, even chosen finite. open problems.