  We study the dominating set reconfiguration problem with the token sliding
rule. It consists, given a graph G=(V,E) and two dominating sets D_s and D_t of
G, in determining if there exists a sequence S=<D_1:=D_s,...,D_l:=D_t> of
dominating sets of G such that for any two consecutive dominating sets D_r and
D_{r+1} with r<t, D_{r+1}=(D_r\ u) U v, where uv is an edge of G.
  In a recent paper, Bonamy et al studied this problem and raised the following
questions: what is the complexity of this problem on circular arc graphs? On
circle graphs? In this paper, we answer both questions by proving that the
problem is polynomial on circular-arc graphs and PSPACE-complete on circle
graphs.
