The field of graph theory and combinatorial optimization is rapidly evolving, with a focus on developing new algorithms and techniques to solve complex problems. Researchers are exploring new directions in tournament solutions, graph separators, and orientation problems. Notably, the query complexity of determining the existence of kings and strong kings in digraphs has been investigated, leading to a deeper understanding of these concepts. Additionally, the frequency of edges in optimal Hamiltonian cycles has been studied, providing new insights into the traveling salesman problem. The development of new algorithms for finding disjoint paths, balanced separators, and vertex sparsifiers in directed graphs is also a key area of research. Some noteworthy papers include: the work on the hardness of finding kings and strong kings, which provides new bounds on the query complexity of these problems. The paper on all-subsets important separators, which presents a new enumeration algorithm and applies it to various problems in directed graphs, is also of particular interest.