The k-core of a graph is a metric used in a wide range of applications, including social network analytics, visualization, and graph coloring. We present two new parallel and scalable algorithms for finding the maximal k-core in a graph. Unlike past approaches, our new algorithms do not rebuild the graph in every iteration - rather, they use a dynamic graph data structure and avoid one of the largest performance penalties of k-core - pruning vertices and edges. We also show how to extend our algorithms to support k-core edge decomposition for different size k-cores found in the graph. While our new algorithms are architecture independent, our implementations target NVIDIA GPUs. When comparing our algorithms against several highly optimized algorithms, including the sequential igraph implementation and the multi-thread ParK implementation, our new algorithms are significantly faster. For finding the maximal k-core in the graph, our new algorithm can be up-to 58× faster the igraph and up-to 4× faster than ParK executed on a 36 core (72 thread) system. For the k-core decomposition algorithm, we saw even greater and more consistent speedups for our algorithm where it was up-to 130× faster than igraph and up-to 8× faster than ParK. Our algorithms were executed on an NVIDIA P100 GPU.