Relate graph-level parameters to colored up-color domination

Investigate the relationship between the graph-level parameters introduced for up-color domination and the colored-graph parameter gamma_{uc}(G,c).

Background

The paper derives inequalities involving classical domination, independent domination, independence, and chromatic parameters alongside the newly defined up-color domination quantities. It leaves open a systematic characterization of how the graph-level parameters relate to gamma_{uc}(G,c) for particular colorings and graph classes.

References

Investigate the relationship between the previously defined parameters and $\gamma_{uc}(G,c)$.

— 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, second Problem environment