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. [4–7] concerning the pebbling number compared to the peb-bling threshold. Keywords:combinatorics, probability theory, graph theory, graph pebbling, pebbling num-ber, pebbling threshold