In on-line computation, the instance of the problem dealt is not
entirely known from the beginning of the solution process, but it
is revealed step-by-step. In this paper we deal with on-line
independent set. On-line models studied until now for this problem
suppose that the input graph is initially empty and revealed
either vertex-by-vertex, or cluster-by-cluster. Here we present a
new on-line model quite different to the ones already studied. It
assumes that a superset of the final graph is initially present
(in our case the complete graph on the order n of the final
graph) and edges are progressively removed until the achievement
of the final graph. Next, we revisit the model introduced in
[Demange, Paradon and Paschos, Lect. Notes Comput. Sci.1963 (2000)
326–334] and study relaxations assuming that some
paying backtracking is allowed.