Counterexamples to a Monotonicity Conjecture for the Threshold Pebbling   Number
  Graph pebbling considers the problem of transforming configurations of discrete pebbles to certain target configurations on the vertices of a graph, using the so-called pebbling move. This paper provides counterexamples to a monotonicity conjecture stated by Hurlbert et al. concerning the pebbling number compared to the pebbling threshold. 
Johan Bj\"orklund and Cecilia Holmgren
math.CO