It looks like this [paper](http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B75GV-4XVBKYN-1W&_user=10&_coverDate=12%2F01%2F2009&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=1315147388&_rerunOrigin=google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=0f60362eab3f7eb4153d0d00c5f53df8) is what you want.  I think the paper gives an algorithm for generating all the *minimal* (under subgraph inclusion) subgraphs connecting the blue vertices (from which it is easy to obtain all such subgraphs).