{"paper":{"title":"Packing 3-vertex Paths In Cubic 3-connected Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander Kelmans","submitted_at":"2009-10-15T03:00:08Z","abstract_excerpt":"A subgraph (a spanning subgraph) of a graph G whose all components are 3-vertex paths is called an L-packing (respectively, an L-factor} of G. We discuss the following old\n  PROBLEM (A. Kelmans, 1984). Is the following claim true?\n  (C) If G is a cubic 3-connected graph, then G has an L-packing that avoids at most two vertices of G.\n  We show, in particular, that claim (C) is equivalent to some seemingly stronger claims (see Theorem 3.1 below).\n  For example, if G is a cubic 3-connected graph and the number of vertices of G is divisible by three, then then the following claims are equivalent: "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2766","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":""},"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"}