  We introduce a model involving two adversaries Buster and Fixer taking turns
modifying a connected graph, where each round consists of Buster deleting a
subset of edges and Fixer responding by adding edges from a reserve set of
weighted edges to leave the graph connected. With the weights representing the
cost for Fixer to use specific reserve edges to reconnect the graph, we provide
a reasonable definition for what should constitute an optimal strategy for
Fixer to keep the graph connected for as long as possible as cheaply as
possible, and prove that a greedy strategy for Fixer satisfies our conditions
for optimality.
