2009/05/19 by David S. Herscovici, Herscovici, David S., Benjamin D. Hester +3
Mathematics · #05C99 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.0905.3197
openalex publication_date 2009/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate generalizations of pebbling numbers and of Graham's pebbling conjecture that pi(GxH) <= pi(G)pi(H), where pi(G) is the pebbling number of the graph G. We develop new machinery to attack the conjecture, which is now twenty years old. We show that certain conjectures imply others that initially appear stronger. We also find counterexamples that show that Sjostrand's theorem on cover pebbling does not apply if we allow the cost of transferring a pebble from one vertex to an adjacent vertex to depend on the edge, and we describe an alternate pebbling number for which Graham's conjecture is demonstrably false.