The field of graph theory and constraint satisfaction is experiencing significant developments, with a focus on understanding the complexity of problems on graphs defined on groups and the richness of non-redundancy in constraint satisfaction problems. Researchers are exploring the boundaries of NP-completeness and the Exponential Time Hypothesis, and making progress in polynomial-time solvability of various problems. Notably, innovative results are emerging in the study of local search problems, hyperpath and minimal separator enumeration, and the classification of conditional non-redundancy. Noteworthy papers include:

• The paper on the complexity of problems on graphs defined on groups, which shows that certain problems cannot be NP-complete unless the Exponential Time Hypothesis is false.
• The work on the richness of CSP non-redundancy, which provides a deeper understanding of non-redundancy and its connections to other important problems in computer science and mathematics.
• The result on finding sparse induced subgraphs on graphs of bounded induced matching treewidth, which generalizes a meta-problem called Maximum-Weight Induced Subgraph of Bounded Treewidth.