The field of graph theory is witnessing significant advancements, with a focus on developing new parameters and techniques to tackle complex problems. One notable direction is the study of temporal graphs, which are graphs with edges labeled with times at which they are active. Researchers are exploring various aspects of temporal graphs, including exploration problems, vertex-interval-membership width, and tree-interval-membership-width. These parameters provide a bound on the number of vertices that need to be tracked at any given time to solve problems, making them tractable. Additionally, there is a growing interest in developing meta-algorithms that can be applied to large families of problems, bypassing the need for involved dynamic programming arguments. Another area of research is the development of new logics, such as Group Order Logic, which extends fixed-point logic with a group-order operator. This logic has been shown to constitute a new candidate logic for polynomial-time computable queries. Noteworthy papers include:

• Bandwidth vs BFS Width in Matrix Reordering, Graph Reconstruction, and Graph Drawing, which introduces a new width parameter, BFS width, and provides approximation quality guarantees for the Cuthull-McKee heuristic.
• A Weight Function Lemma Heuristic for Graph Pebbling, which introduces a novel heuristic method for refining the selection of balanced strategies to improve bounds for the pebbling number.