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Traditionally, reconfiguration problems ask the question whether a givensolution of an optimization problem can be transformed to a target solution ina sequence of small steps that preserve feasibility of the intermediatesolutions. In this paper, rather than asking this question from an algorithmicperspective, we analyze the combinatorial structure behind it. We consider theproblem of reconfiguring one independent set into another, using two differentprocesses: (1) exchanging exactly $k$ vertices in each step, or (2) removing oradding one vertex in each step while ensuring the intermediate sets contain atmost $k$ fewer vertices than the initial solution. We are interested indetermining the minimum value of $k$ for which this reconfiguration ispossible, and bound these threshold values in terms of several structural graphparameters. For hereditary graph classes we identify structures that cause thereconfiguration threshold to be large.

Independent Set Reconfiguration Thresholds of Hereditary Graph Classes