She does actually need the DUP even to maintain a minority government, Nigel. Without their support she cannot hope to get a majority for the Queens Speech, and would have to resign, and Jeremy Corbyn would be invited to have a go at forming a government. Quite what would happen if he couldn't succeed isn't too clear. The assumption has been that if that situation arose, where no one could get to majority for essential purposes, there'd be another election.

There aren't really any precedents for the present situation. Even with DUP support, I make it that, if Sinn Fein were to decide to take their seats, the May government would have a majority of two. It's not too likely that Sinn Fein will abandon their longstanding policy of not taking sears, but these are strange times, and it could be argued that by continuing this policy they are in effect assisting this "Conservative and Unionist" administration to survive.