The field of online algorithms and graph theory is experiencing significant developments, with a focus on improving the efficiency and accuracy of various algorithms. Researchers are exploring new approaches to solve classic problems, such as online bipartite matching and graph coloring, and are making progress in understanding the limitations and possibilities of these algorithms. Additionally, there is a growing interest in developing scalable and provable methods for computing important graph metrics, such as the Kemeny constant. Noteworthy papers include:

• Online Graph Coloring for k-Colorable Graphs, which presents significant improvements to the current upper bounds for online graph coloring.
• Scalable and Provable Kemeny Constant Computation on Static and Dynamic Graphs, which proposes a new approach for approximating the Kemeny constant via 2-forest sampling, achieving better theoretical bounds and near-linear time complexity.