Concurrency control is one of the most performance critical steps in modern many-core database systems. Achieving higher throughput on multi-socket servers is difficult and many concurrency control algorithms reduce the amount of accepted schedules in favor of transaction throughput or relax the isolation level which introduces unwanted anomalies. Both approaches lead to unexpected transaction behavior that is difficult to understand by the database users. We introduce a novel multi-version concurrency protocol that achieves high performance while reducing the number of aborted schedules to a minimum and providing the best isolation level. Our approach leverages the idea of a graph-based scheduler that uses the concept of conflict graphs. As conflict serializable histories can be represented by acyclic conflict graphs, our scheduler maintains the conflict graph and allows all transactions that keep the graph acyclic. All conflict serializable schedules can be accepted by such a graph-based algorithm due to the conflict graph theorem. Hence, only transaction schedules that truly violate the serializability constraints need to abort. Our developed approach is able to accept the useful intersection of commit order preserving conflict serializable (COCSR) and recoverable (RC) schedules which are the two most desirable classes in terms of correctness and user experience. We show experimentally that our graph-based scheduler has very competitive throughput in pure transactional workloads while providing fewer aborts and improved user experience. Our multi-version extension helps to efficiently perform long-running read transactions on the same up-to-date database. Moreover, our graph-based scheduler can outperform the competitors on mixed workloads.