—Due to the potential of enhancing traffic safety, protecting environment, and enabling new applications, vehicular communications, especially vehicle-to-vehicle (V2V) communications, has recently been receiving much attention. Because of both safety and non-safety real-time applications, V2V communications has QoS requirements on rate, latency, and reliability. How to appropriately design channel allocation is therefore a key MAC/PHY layer issue in vehicular communications. The QoS requirements of real-time V2V communications can be met by achieving a low outage probability and high outage capacity. In this paper, we first formulate the subchannel allocation in V2V communications into a maximum matching problem on random bipartite graphs. A distributed shuffling based Hopcroft-Karp (DSHK) algorithm will then be proposed to solve this problem with a sub-linear complexity of O(N2/3 ), where N is the number of subchannels. By studying the maximum matching generated by the DSHK algor...