A cop-robber guarding game is played
by the robber-player and the cop-player on a graph $G$ with
a bipartition $\{R,C\}$ of the vertex set.
The robber-player starts the game by placing
a robber (her pawn) on a vertex in $R$, followed
by the cop-player who place a set of cops (her pawns)
on some vertices in $C$.
They take turns in moving their pawns to adjacent vertices.
The cop-player moves the cops within $C$ to prevent
the robber-player from moving the robber to any vertex in $C$.
The robber-player wins if it gets a turn
to move the robber onto a vertex in $C$
on which no cops situate, and the cop-player wins otherwise.
The problem is to find the minimum number of cops that
admit a winning strategy to the cop-player.
It has been shown that the problem is polynomially solvable
if $R$ induces a path, whereas it is NP-complete
if $R$ induces a tree.
It was open whether it is solvable or not
when $R$ induces a cycle.
This paper answers the question affirmatively.