{"paper":{"title":"Parameterized Complexity of the Star Decomposition Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Ramin Javadi, Sahab Hajebi","submitted_at":"2024-11-20T14:19:30Z","abstract_excerpt":"A star of length $ \\ell $ is defined as the complete bipartite graph $ K_{1,\\ell } $. In this paper we deal with the problem of edge decomposition of graphs into stars of varying lengths.\n  Given a graph $ G $ and a list of integers $S=(s_1,\\ldots, s_t) $, an $S$-star decomposition of $ G $ is an edge decomposition of $ G $ into graphs $G_1 ,G_2 ,\\ldots,G_t $ such that $G_i$ is isomorphic to an star of length $s_i$, for each $i \\in\\{1,2,\\ldots,t\\}$. Given a graph $G$ and a list of integers $S$, the \\sdp problem asks if $G$ admits an $ S $-star decomposition. The problem is known to be NP-compl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13348","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.13348/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}