Pebbling graphs
The pebbling number \(f(G)\) of a graph \(G\) is the least \(n\) such that, however \(n\) pebbles are placed on the vertices of \(G\), we can move a pebble to any vertex by a sequence of moves, each move taking two pebbles off one vertex and placing one on an adjacent vertex. Ronald Graham conjectured that for all graphs \(G\) and \(H\), \(f(G\times H)\leq f(G)\cdot f(H)\). This paper proves that this conjecture is true if \(G\) and \(H\) are trees.
scientific article; zbMATH DE number 130571