New graph theory solution to the transplant recipient matching problem:

People are born with two kidneys but need only one to survive. That can be a blessing for those with two failed kidneys, because sometimes they can receive a donated kidney from a family member. But the good fortune can turn bitter: a third of the time, the donor and the recipient aren't a compatible match.

One solution is to arrange a kind of surgical double-date. When two donor-recipient pairs are in the same predicament of incompatibility, it can happen that the donor of one pair is a good match for the recipient of the other, and vice versa. Doctors and lawmakers are working to create a national database of kidney donation pairs that could vastly improve the chances of finding such matches.

Multiple transplants involving more than two pairs are possible, and have occasionally been performed, but the complex logistics of such procedures ensure that they can happen only rarely. But even matching up two pairs raises difficult questions about how to find the matches. A new mathematical study shows how to match up the maximum number of donors with recipients while simultaneously guaranteeing high compatibility in each case.