  Recently, Sato et al. proposed an public verifiable blind quantum computation
(BQC) protocol by inserting a third-party arbiter. However, it is not true
public verifiable in a sense, because the arbiter is determined in advance and
participates in the whole process. In this paper, a public verifiable protocol
for measurement-only BQC is proposed. The fidelity between arbitrary states and
the graph states of 2-colorable graphs is estimated by measuring the
entanglement witnesses of the graph states,so as to verify the correctness of
the prepared graph states. Compared with the previous protocol, our protocol is
public verifiable in the true sense by allowing other random clients to execute
the public verification. It also has greater advantages in the efficiency,
where the number of local measurements is O(n^3*log {n}) and graph states'
copies is O(n^2*log{n}).
