The stable roommate problem asks whether an even number of participants, each with a strict ranking of all other participants, can be paired so that there is no blocking pair. A blocking pair consists of two participants who each prefer the other to their assigned partner. The desired pairing is a perfect matching. Unlike the stable marriage problem, a stable roommate instance need not have a solution (Young and Studebaker 2026).
Let 
be the probability that a solution exists when the
participants have independent, uniformly random strict rankings. Young and Studebaker
(2026) reported
 |
as even 
, where 
is the gamma function.
The leading constant is approximately 2.234914123. This confirms Mertens's predicted
exponent but not his original numerical prediction for the constant (Young and Studebaker
2026).
