Our input is a complete graph G=(V,E) on n vertices where each vertex
has a strict ranking of all other vertices in G. Our goal is to construct a
matching in G that is popular. A matching M is popular if M does not lose
a head-to-head election against any matching M′, where each vertex casts a
vote for the matching in {M,M′} where it gets assigned a better partner.
The popular matching problem is to decide whether a popular matching exists or
not. The popular matching problem in G is easy to solve for odd n.
Surprisingly, the problem becomes NP-hard for even n, as we show here.Comment: Appeared at FSTTCS 201