Compute graph-level up-color domination parameters

Develop algorithms to compute the graph-level up-color domination number Gamma_{uc}(G) and the chromatic up-color domination number chi_{uc}(G) for specific graph families, and analyze the computational complexity of computing these parameters for general graphs.

Background

The paper establishes computational hardness for several fixed-coloring and coloring-optimization variants, while providing polynomial-time algorithms on trees for fixed colorings. It explicitly leaves the development of algorithms for the graph-level parameters and the general complexity analysis as future work.

References

Develop algorithms to compute $\gamma_{uc}(G)$ and $\chi_{uc}(G)$ for specific graph families and analyze the computational complexity of these problems for general graphs.

— Domination on Vertex-weighted Graphs Induce by a Coloring  (2502.07248 - Garrido-Vizuete et al., 11 Feb 2025) in Section 5, Conclusions and open problems, third Problem environment