{"paper":{"title":"The Bollob\\'as-Eldridge-Catlin conjecture for even girth at least $10$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ross J. Kang, Wouter Cames van Batenburg","submitted_at":"2017-03-15T13:36:10Z","abstract_excerpt":"Two graphs $G_1$ and $G_2$ on $n$ vertices are said to \\textit{pack} if there exist injective mappings of their vertex sets into $[n]$ such that the images of their edge sets are disjoint. A longstanding conjecture due to Bollob\\'as and Eldridge and, independently, Catlin, asserts that, if $(\\Delta(G_1)+1) (\\Delta(G_2)+1) \\le n+1$, then $G_1$ and $G_2$ pack. We consider the validity of this assertion under the additional assumptions that neither $G_1$ nor $G_2$ contain a $4$-, $6$- or $8$-cycle, and that $\\Delta(G_1)$ or $\\Delta(G_2)$ is large enough ($\\ge 940060$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05149","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"}