{"paper":{"title":"Pebbling on Directed Graphs with Fixed Diameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Franklin Kenter, John Asplund","submitted_at":"2018-09-07T17:15:38Z","abstract_excerpt":"Pebbling is a game played on a graph. The single player is given a graph and a configuration of pebbles and may make pebbling moves by removing 2 pebbles from one vertex and placing one at an adjacent vertex to eventually have one pebble reach a predetermined vertex. The pebbling number, $\\pi(G)$, is the minimum number of pebbles such that regardless of their exact configuration, the player can use pebbling moves to have a pebble reach any predetermined vertex.\n  Previous work has related $\\pi(G)$ to the diameter of $G$. Clarke, Hochberg, and Hurlbert demonstrated that every connected undirect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02582","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"}