{"paper":{"title":"Combined degree and connectivity conditions for H-linked graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Florian Pfender","submitted_at":"2012-06-07T09:15:40Z","abstract_excerpt":"For a given multigraph H, a graph G is H-linked, if |G| \\geq |H| and for every injective map {\\tau}: V (H) \\rightarrow V (G), we can find internally disjoint paths in G, such that every edge from uv in H corresponds to a {\\tau} (u) - {\\tau} (v) path. To guarantee that a G is H-linked, you need a minimum degree larger than |G|/2. This situation changes, if you know that G has a certain connectivity k. Depending on k, even a minimum degree independent of |G| may suffice. Let {\\delta}(k, H, N) be the minimum number, such that every k-connected graph G with |G| = N and {\\delta}(G) \\geq {\\delta}(k,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1427","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"}