  In this paper we study the mincut problem in the online setting. We consider
two distinct models: A) competitive analysis and B) regret analysis. In the
competitive setting we consider the vertex arrival model; whenever a new vertex
arrives it's neighborhood with respect to the set of known vertices is
revealed. An online algorithm must make an irrevocable decision to determine
the side of the cut that the vertex must belong to in order to minimize the
size of the final cut. Various models are considered. 1) For classical and
advice models we give tight bounds on the competitive ratio of deterministic
algorithms. 2) Next we consider few semi-adversarial inputs: random order of
arrival with adversarially generated and sparse graphs. 3) Lastly we derive
some structural properties of \mc-type problems with respect to greedy
strategies.
  Finally we consider a non-stationary regret setting with a variational budget
$V_T$ and give tights bounds on the regret function. Specifically, we show that
if $V_T$ is sublinear in $T$ (number of rounds) then there is a deterministic
algorithm achieving a sublinear regret bound ($O(V_T)$). Further, this is
optimal, even if randomization is allowed.
