{"paper":{"title":"Packing large trees of consecutive orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrzej \\.Zak","submitted_at":"2015-10-26T13:17:09Z","abstract_excerpt":"A conjecture by Bollob\\'as from 1995 (which is a weakenning of the famous Tree Packing Conjecture by Gy\\'arf\\'as from 1976) states that any set of $k$ trees $T_n,T_{n-1},\\dots,T_{n-k+1}$, such that $T_{n-i}$ has $n-i$ vertices, pack into $K_n$, provided $n$ is sufficiently large. We confirm Bollob\\'as conjecture for trees $T_n,T_{n-1},\\dots,T_{n-k+1}$, such that $T_{n-i}$ has $k-1-i$ leaves or a pending path of order $k-1-i$. As a consequence we obtain that the conjecture is true for $k\\leq 5$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07467","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"}