{"paper":{"title":"Immersing complete digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bojan Mohar, Diego Scheide, Jessica McDonald, Matt DeVos","submitted_at":"2011-09-17T00:59:26Z","abstract_excerpt":"We consider the problem of immersing the complete digraph on t vertices in a simple digraph. For Eulerian digraphs, we show that such an immersion always exists whenever minimum degree is at least t(t-1), and for t at most 4 minimum degree at least t-1 suffices. On the other hand, we show that there exist non-Eulerian digraphs with all vertices of arbitrarily high in- and outdegree which do not contain an immersion of the complete digraph on 3 vertices. As a side result, we obtain a construction of digraphs with large outdegree in which all cycles have odd length, simplifying a former construc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3741","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"}