Relation between binary fractions and host clusters. Panels a–c: total binary fraction as a function of cluster dynamical age, i.e., age normalized over the half-mass relaxation time, total cluster mass, and central density in stars pc⁻². Azure lines and shaded regions indicate the straight line that best fits the data and its 1σ dispersion. The values of Spearman’s rank coefficient (ρ) and the corresponding p-values are indicated in the top-left corner of each plot. Panels b1–b3: same as panel b, but with clusters grouped into three dynamical age groups, defined as young, intermediate, and old clusters. Panels c1–c3: same as panel c, for the three groups of clusters.