{"paper":{"title":"A Variation of the Erd\\H{o}s-S\\'os Conjecture in Bipartite Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Long-tu Yuan, Xiao-Dong Zhang","submitted_at":"2017-02-10T03:53:20Z","abstract_excerpt":"The Erd\\H{o}s-S\\'{o}s Conjecture states that every graph with average degree more than $k-2$ contains all trees of order $k$ as subgraphs. In this paper, we consider a variation of the above conjecture: studying the maximum size of an $(n,m)$-bipartite graph which does not contain all $(k,l)$-bipartite trees for given integers $n\\ge m$ and $k\\ge l$. In particular, we determine that the maximum size of an $(n,m)$-bipartite graph which does not contain all $(n,m)$-bipartite trees as subgraphs (or all $(k,2)$-bipartite trees as subgraphs, respectively). Furthermore, all these extremal graphs are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03060","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"}