The chromatic villainy 
of a graph 
is the largest number of vertices
that must be recolored to repair a rearrangement of an optimal vertex
coloring, while preserving the number of vertices
of each color. The maximum is over optimal vertex
colorings and all rearrangements. Weak chromatic villainy allows the repair to
change these color multiplicities (Jiang et al. 2026).
Jiang et al. (2026) proved that the cycle graph 
has 
for 
. For a feasible three-color profile with multiplicities
,
,
and 
,
both the ordinary and weak repair radii are 
, where 
is the floor function.
Jiang et al. (2026) also give exact finite formulas for both parameters on
arbitrary complete multipartite graphs.
