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Vehicle-to-vehicle (V2V) communications are considered to be a significant step forward toward a highly secure and efficient intelligent transportation system. In this paper, we propose the use of graph theory to formulate the problem of cooperative communications scheduling in vehicular networks. In lieu of exhaustive search with intractable complexity for the maximum sum rate (MSR), we propose a bipartite-graph-based (BG) scheduling scheme to allocate the vehicle-to-infrastructure (V2I) and V2V links for both single-hop and dual-hop communications. The Kuhn-Munkres (KM) algorithm is adopted to solve the problem of maximum weighted matching (MWM) of the constructed BG. Simulation results indicate that the proposed scheme performs extremely close to the optimal scheme and results in better fairness among vehicle users with considerably lower computational complexity. Moreover, cooperative communications can improve both the throughput and spectral efficiency (SE) of vehicular networks.