{"paper":{"title":"Pebbling and Optimal Pebbling in Graphs","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"D. B. West, D. Cranston, D. P. Bunde, E. W. Chambers, K. Milans","submitted_at":"2005-10-28T05:27:13Z","abstract_excerpt":"Given a distribution of pebbles on the vertices of a graph G, a {\\it pebbling move} takes two pebbles from one vertex and puts one on a neighboring vertex. The {\\it pebbling number} \\Pi(G) is the minimum k such that for every distribution of k pebbles and every vertex r, it is possible to move a pebble to r. The {\\it optimal pebbling number} \\Pi_{OPT}(G) is the minimum k such that some distribution of k pebbles permits reaching each vertex.\n  We give short proofs of prior results on these parameters for paths, cycles, trees, and hypercubes, a new linear-time algorithm for computing \\Pi(G) on t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0510621","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}