Improved pebbling bounds |
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Authors: | Melody Chan |
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Institution: | a Department of Mathematics, Princeton University, Princeton, NJ 08544, USA b Department of Mathematics, East Tennessee State University, Johnson City, TN 37614, USA |
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Abstract: | Consider a configuration of pebbles distributed on the vertices of a connected graph of order n. A pebbling step consists of removing two pebbles from a given vertex and placing one pebble on an adjacent vertex. A distribution of pebbles on a graph is called solvable if it is possible to place a pebble on any given vertex using a sequence of pebbling steps. The pebbling number of a graph, denoted f(G), is the minimal number of pebbles such that every configuration of f(G) pebbles on G is solvable. We derive several general upper bounds on the pebbling number, improving previous results. |
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Keywords: | 05C99 |
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