  Graph pebbling is a network optimization model for satisfying vertex demands
with vertex supplies (called pebbles), with partial loss of pebbles in transit.
The pebbling number of a demand in a graph is the smallest number for which
every placement of that many supply pebbles satisfies the demand. The Target
Conjecture (Herscovici-Hester-Hurlbert, 2009) posits that the largest pebbling
number of a demand of fixed size $t$ occurs when the demand is entirely stacked
on one vertex. This truth of this conjecture could be useful for attacking many
open problems in graph pebbling, including the famous conjecture of Graham
(1989) involving graph products. It has been verified for complete graphs,
cycles, cubes, and trees. In this paper we prove the conjecture for 2-paths and
Kneser graphs over pairs.
