Threshold and complexity results for the cover pebbling game

Given a configuration of pebbles on the vertices of a graph, a pebbling move is defined by removing two pebbles from some vertex and placing one pebble on an adjacent vertex. The cover pebbling number of a graph, γ ( G ) , is the smallest number of pebbles such that through a sequence of pebbling moves, a pebble can eventually be placed on every vertex simultaneously, no matter how the pebbles are initially distributed. We determine Bose–Einstein and Maxwell–Boltzmann cover pebbling thresholds for the complete graph. Also, we show that the cover pebbling decision problem is NP-complete.