Pebbling in Planar Graphs

Student Author(s)

Timothy Lewis

Faculty Mentor(s)

Dr. Charles Cusack

Document Type


Event Date



Given a simple connected graph, a pebbling configuration is a function from its vertex set to the nonnegative integers. A pebbling move between adjacent vertices removes two pebbles from one vertex and adds one pebble to the other. A vertex r is said to be reachable from a configuration if there exists a sequence of pebbling moves that places at least one pebble on r. A configuration is solvable if every vertex is reachable. We prove that determining reachability of a vertex is NP-complete, even in graphs that are planar. We also prove that reachability of a vertex can be determined in O(n6 ) time in planar graphs of diameter two.

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