OFDMA is a potential technology that can flexibly allocate subcarriers while providing diversity gain to multiple users. In our recent work , we showed a surprising result that the maximum frequency diversity gain in OFDMA systems is equal to the number of independent subcarriers, i.e., the same as that in point-to-point OFDM systems despite of the fact that multiple users will share a common set of subcarriers. However, the diversity gain only characterizes the first-order outage performance in the high SNR regime, and the outage performance in the low SNR regime, which is very important in practice, is still an open problem. In this paper, we first formulate the subcarrier allocation problem in OFDMA systems as a random bipartite graph model. Then, a more precise outage probability is derived in the high SNR regime using a high-order analysis of the maximum matching on a random bipartite graph. An approximate outage probability in the low SNR regime is also obtained by studying the complement of a random bipartite graph. It is then demonstrated that the coefficient of the second-order term in the outage probability expression is zero except for the scenario of two users with two or three subcarriers.