In this paper, we present multi-threaded algorithms for graph coloring suitable to the shared memory programming model. We modify an existing algorithm widely used in the literature and prove the correctness of the modified algorithm. We also propose a new approach to solve the problem of coloring using locks. Using datasets from real world graphs, we evaluate the performance of the algorithms on the Intel platform. We compare the performance of the sequential approach v/s our proposed approach and analyze the speedup obtained against the existing algorithm from the literature. The results show that the speedup obtained is consequential. We also provide a direction for future work towards improving the performance further in terms of different metrics.