We study a game of pursuit and evasion introduced by Seager in 2012, in which
a cop searches the robber from outside the graph, using distance queries. A
graph on which the cop wins is called locatable. In her original paper, Seager
asked whether there exists a characterisation of the graph property of
locatable graphs by either forbidden or forbidden induced subgraphs, both of
which we answer in the negative. We then proceed to show that such a
characterisation does exist for graphs of diameter at most 2, stating it
explicitly, and note that this is not true for higher diameter. Exploring a
different direction of topic, we also start research in the direction of
colourability of locatable graphs, we also show that every locatable graph is
4-colourable, but not necessarily 3-colourable.Comment: 25 page