  We introduce a new positional game called `Toucher-Isolator', which is a
quantitative version of a Maker-Breaker type game. The playing board is the set
of edges of a given graph G, and the two players, Toucher and Isolator, claim
edges alternately. The aim of Toucher is to `touch' as many vertices as
possible (i.e. to maximise the number of vertices that are incident to at least
one of her chosen edges), and the aim of Isolator is to minimise the number of
vertices that are so touched.
  We analyse the number of untouched vertices u(G) at the end of the game when
both Toucher and Isolator play optimally, obtaining results both for general
graphs and for particularly interesting classes of graphs, such as cycles,
paths, trees, and k-regular graphs. We also provide tight examples.
