{"paper":{"title":"Modified Linear Programming and Class 0 Bounds for Graph Pebbling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carl Yerger, Chenxiao Xue, Daniel W. Cranston, Luke Postle","submitted_at":"2015-08-28T18:11:47Z","abstract_excerpt":"Given a configuration of pebbles on the vertices of a connected graph $G$, a \\emph{pebbling move} removes two pebbles from some vertex and places one pebble on an adjacent vertex. The \\emph{pebbling number} of a graph $G$ is the smallest integer $k$ such that for each vertex $v$ and each configuration of $k$ pebbles on $G$ there is a sequence of pebbling moves that places at least one pebble on $v$.\n  First, we improve on results of Hurlbert, who introduced a linear optimization technique for graph pebbling. In particular, we use a different set of weight functions, based on graphs more genera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07299","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"}