  We consider the problem of searching for an unknown target vertex $t$ in a
(possibly edge-weighted) graph. Each \emph{vertex-query} points to a vertex $v$
and the response either admits $v$ is the target or provides any neighbor
$s\not=v$ that lies on a shortest path from $v$ to $t$. This model has been
introduced for trees by Onak and Parys [FOCS 2006] and for general graphs by
Emamjomeh-Zadeh et al. [STOC 2016]. In the latter, the authors provide
algorithms for the error-less case and for the independent noise model (where
each query independently receives an erroneous answer with known probability
$p<1/2$ and a correct one with probability $1-p$).
  We study this problem in both adversarial errors and independent noise
models. First, we show an algorithm that needs $\frac{\log_2 n}{1 - H(r)}$
queries against \emph{adversarial} errors, where adversary is bounded with its
rate of errors by a known constant $r<1/2$. Our algorithm is in fact a
simplification of previous work, and our refinement lies in invoking
amortization argument. We then show that our algorithm coupled with Chernoff
bound argument leads to an algorithm for independent noise that is simpler and
with a query complexity that is both simpler and asymptotically better to one
of Emamjomeh-Zadeh et al. [STOC 2016].
  Our approach has a wide range of applications. First, it improves and
simplifies Robust Interactive Learning framework proposed by Emamjomeh-Zadeh et
al. [NIPS 2017]. Secondly, performing analogous analysis for
\emph{edge-queries} (where query to edge $e$ returns its endpoint that is
closer to target) we actually recover (as a special case) noisy binary search
algorithm that is asymptotically optimal, matching the complexity of Feige et
al. [SIAM J. Comput. 1994]. Thirdly, we improve and simplify upon existing
algorithm for searching of \emph{unbounded} domains due to Aslam and Dhagat
[STOC 1991].
