It looks like both Facebook and Yahoo are going to cosy up with each other to try and form a future partnership. The rationale between such a partnership is due to the fact that Facebook want better search functionality for its users and since Google is out of the question (with their mediocre attempt of social media Google+) Facebook turned to Yahoo’s expertise to help them out of this problem.
Facebook founder Mark Zuckerberg has commented in the past saying "Facebook is pretty uniquely positioned to answer a lot of questions people have 'what sushi restaurant friends like'. These are queries you could potentially do on Facebook if we built it out ... at some point we'll do it ... we have a team working on search"
What is in it for Yahoo I hear you say, well, for the search engine who in recent years has been losing market share it would give it a much needed boast in users, around 1 billion of Facebook’s subscribers; which will help it pinch some market share from the all-powerful Google search (66% market share).
AllThingsD have discredited such a proposal as it quotes its own sources saying that due to the alliance between Microsoft and Yahoo any alliance between Facebook and Yahoo could never go ahead.