Graph Covering and Subgraph Problems

Combinatorial optimization problems and graph theory play an important role in several fields including logistics, artificial intelligence, software engineering, etc. In this paper, we explore a subset of combinatorial graph problems which we placed into two groups, namely, graph covering and subgraph problems. Here, the former include well-known dominating set and vertex cover problem, and the latter include clique and independent set problem. For each problem we give its definition, report state-of-the-art exact algorithms as well as heuristic and approximation algorithms, and list real-world applications if we were able to obtain any. At the end of the paper, we also relate the problems among each other.