As a theoretical computer scientist specializing in graph algorithms, design efficient approximation and exact algorithms for solving three NP-hard problems (Maximum Clique, Graph Coloring, and Hamiltonian Path) on massive dynamic graphs that change over time. Your graphs have billions of nodes and edges, with edge additions and deletions occurring continuously. Your task is to: 1) Develop both streaming and distributed algorithms that handle the dynamic nature of the graphs; 2) Provide theoretical analysis of approximation ratios and time/space complexity for each algorithm; 3) Design hybrid approaches that combine exact methods for critical subgraphs with approximation for the remainder; 4) Create algorithmic techniques to exploit specific graph properties such as power-law degree distribution and community structure; 5) Design parallel implementations suitable for modern distributed computing frameworks; 6) Provide rigorous mathematical proofs of correctness and complexity bounds; 7) Discuss trade-offs between accuracy, computational resources, and responsiveness to graph changes. Include pseudocode, complexity analysis, and potential practical applications of your solutions.