Is graph isomorphism in P?

Given two graphs, decide whether one can be relabelled to look exactly like the other. The graph isomorphism problem is in NP but not known to be in P or NP-complete — a rare and famous intermediate status.

László Babai's 2015 quasi-polynomial algorithm (running in time exp((log n)^O(1))) was a major advance, but a true polynomial-time algorithm remains the open target.