{"paper":{"title":"Advances on the Conjecture of Erd\\H{o}s-S\\'os for spiders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Camino Balbuena, Jos\\'e R. Portillo, Mucuy-Kak Guevara, Pedro Reyes","submitted_at":"2017-06-11T21:49:13Z","abstract_excerpt":"- A hamiltonian graph $G$ verifying $e(G)>n(k-1)/2$ %with a vertex of degree greater or equal than $k$ contains any $k$-spider.\n  - If $G$ is a graph with average degree $\\bar{d} > k-1$, then every spider of size $k$ is contained in $G$ for $k\\le 10$.\n  - A $2$-connected graph with average degree $\\bar{d} > \\ell_2+\\ell_3+\\ell_4$ contains every spider of $4$ legs $S_{1,\\ell_2,\\ell_3,\\ell_4}$. We claim also that the condition of $2$-connection is not needed, but the proof is very long and it is not included in this document."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03414","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"}