Color palettes are widely used by artists to define colors of artworks and explore color designs. In general, artists select the colors of a palette by following a set of rules, eg contrast or relative luminance. Existing interactive palette exploration tools explore palette spaces following limited constraints defined as geometric configurations in color space eg{} harmony rules on the color wheel.Palette search algorithms sample palettes from color relations learned from an input dataset, however they cannot provide interactive user edits and palette refinement.We introduce in this work a new versatile formulation enabling the creation of constraint-based interactive palette exploration systems. Our technical contribution is a graph-based palette representation, from which we define palette exploration as a minimization problem that can be solved efficiently and provide real-time feedback. Based on our formulation, we introduce two interactive palette exploration strategies: constrained palette exploration, and for the first time, constrained palette interpolation. We demonstrate the performances of our approach on various application cases and evaluate how it helps users finding trade-offs between concurrent constraints.