The field of graph partitioning and clustering is moving towards more complex and realistic models, with a focus on overlapping clusters and vertex splitting. Researchers are exploring new algorithms and techniques to tackle these challenges, including fixed-parameter tractability and approximation algorithms. Notable progress has been made in solving variants of classic problems, such as Cluster Deletion and Clique Partition, on specific graph classes like cographs and permutation graphs. Meanwhile, the study of distinguishing problems like Planted Clique is deepening our understanding of the limits of efficient algorithms. Some papers are particularly noteworthy, including:

• A paper that presents a much simpler proof of a theorem on Cluster Deletion on cographs and investigates the problem on permutation graphs, also providing a polynomial-time algorithm for Clique Partition on graphs with bounded clique number.
• A paper that shows the optimality of low-degree polynomials for distinguishing Planted Clique distributions and introduces a harder planted distribution that is much more challenging to distinguish.