Pebbling in Kneser Graphs
摘要
Graph pebbling is a game played on graphs with pebbles on their vertices. A pebbling move removes two pebbles from one vertex and places one pebble on an adjacent vertex. The pebbling number \(\pi (G)\) is the smallest t so that from any initial configuration of t pebbles it is possible, after a sequence of pebbling moves, to place a pebble on any given target vertex. We consider the pebbling number of Kneser graphs, and give positive evidence for the conjecture that every Kneser graph has pebbling number equal to its number of vertices.