{"paper":{"title":"Line-Broadcasting in Complete k-Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Revital Hollander Shabtai, Yehuda Roditty","submitted_at":"2015-04-09T20:29:22Z","abstract_excerpt":"A line-broadcasting model in a connected graph $G=(V,E)$, $|V|=n$, is a model in which one vertex, called the {\\it originator} of the broadcast holds a message that has to be transmitted to all vertices of the graph through placement of a series of calls over the graph. In this model, an informed vertex can transmit a message through a path of any length in a single time unit, as long as two transmissions do not use the same edge at the same time. Farley \\cite{f} has shown that the process is completed within at most $\\lceil \\log_{2}n \\rceil$ time units from any originator in a tree (and thus "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02491","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"}