Roadmap Combinatorics and Algebra Research Group:

Topic 1. Graph Labeling.

2025-2026: Characterization of various graph labelings and graph colorings.
2027-2028: Applications of various graph labelings and graph colorings.

Topic 2. Ramsey Theory.

2025-2026: Computation of edge Ramsey numbers or construction of minimal Ramsey graphs involving small graphs.
2027-2028: Computation of edge Ramsey numbers or construction of minimal Ramsey graphs for pairs of specific graph classes.

Topic 3. Metric Dimension.

2025-2026: Computation of various types of metric dimension, partition dimension, and multiset dimension.
2027-2028: Characterization of graphs having a given partition dimension or (outer) multiset dimension for specific classes of graphs.

Topic 4. Hopf Algebra.

2025-2026: Yetter–Drinfeld modules and Drinfeld centers, bi-Galois co-objects, and Hopf categories.
2027-2028: Properties of the Drinfeld center relative to module categories, and 2-Morita equivalence between bicategories of module categories.

Topic 5. Commutative Algebra.

2025-2026: Algebraic properties of ideals in polynomial rings associated with certain graphs.
2027-2028: Homological properties of ideals in polynomial rings associated with certain graphs.