2005/10/18 by Anant P. Godbole, Godbole, Anant P., Nathaniel G. Watson +3
Mathematics · #03D13 #05C70 #05C99 #91A43 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:03D13 #msc:05C70 #msc:05C99 #msc:91A43
paper · pdf · doi:10.48550/arxiv.math/0510394
23 pages
arxiv created 2005/10/18 · arxiv updated 2009/12/01
Given a configuration of pebbles on the vertices of a graph, a pebbling move is defined by removing two pebbles from some vertex and placing one pebble on an adjacent vertex. The cover pebbling number of a graph is the smallest number of pebbles necessary so that through a sequence of pebbling moves, a pebble can eventually be placed on every vertex simultaneously, no matter how the pebbles are initially distributed. We determine Bose Einstein and Maxwell Boltzmann cover pebbling thresholds for the complete graph. Also, we show that the cover pebbling decision problem is NP-complete.