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The Complexity of Pebbling and Cover Pebbling

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arxiv math/0503511 v3 pith:UKCYCA6B submitted 2005-03-24 math.CO

classification math.CO
keywords pebblingcovercomplexityconfigurationdefinitiondeterminingtraditionalaccording
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This paper discusses the complexity of graph pebbling, dealing with both traditional pebbling and the recently introduced game of cover pebbling. Determining whether a configuration is solvable according to either the traditional definition or the cover pebbling definition is shown to be NP-complete. The problem of determining the cover pebbling number for an arbitrary demand configuration is shown to be NP-hard.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The only Class 0 Flower snark is the smallest

    math.CO 2025-05 conditional novelty 6.0 of 10

    J_3, the smallest Flower snark, is Class 0 with pebbling number 12, making it the only Class 0 Flower snark.

  2. A Weight Function Lemma Heuristic for Graph Pebbling

    cs.DM 2025-05 conditional novelty 6.0 of 10

    A new heuristic for building Weight Function Lemma strategies improves the best-known pebbling-number upper bounds for Blanuša 2 (30 vs 34) and Flower snarks Jm for m ≥ 5.

  3. Applying Hurlbert's Linear Optimization Technique to Establish Bounds on Pebbling Numbers

    math.CO 2025-09 reject novelty 1.0 of 10

    The paper re-derives known pebbling number bounds for the Petersen graph, the Bruhat graph B4, and trees using Hurlbert's linear optimization technique with hand-chosen weight functions, without introducing new results.

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