{"paper":{"title":"Constructing graphs with no immersion of large complete graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Karen L. Collins, Megan E. Heenehan","submitted_at":"2012-06-07T16:29:21Z","abstract_excerpt":"In 1989, Lescure and Meyniel proved, for $d=5, 6$, that every $d$-chromatic graph contains an immersion of $K_d$, and in 2003 Abu-Khzam and Langston conjectured that this holds for all $d$. In 2010, DeVos, Kawarabayashi, Mohar, and Okamura proved this conjecture for $d = 7$. In each proof, the $d$-chromatic assumption was not fully utilized, as the proofs only use the fact that a $d$-critical graph has minimum degree at least $d - 1$. DeVos, Dvo\\v{r}\\'ak, Fox, McDonald, Mohar, and Scheide show the stronger conjecture that a graph with minimum degree $d-1$ has an immersion of $K_d$ fails for $d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1545","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"}