{"paper":{"title":"Packing and Covering Immersion Models of Planar subcubic Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Archontia Giannopoulou, Dimitrios M. Thilikos, Jean-Florent Raymond, O-joung Kwon","submitted_at":"2016-02-12T13:14:08Z","abstract_excerpt":"A graph $H$ is an immersion of a graph $G$ if $H$ can be obtained by some sugraph $G$ after lifting incident edges. We prove that there is a polynomial function $f:\\Bbb{N}\\times\\Bbb{N}\\rightarrow\\Bbb{N}$, such that if $H$ is a connected planar subcubic graph on $h>0$ edges, $G$ is a graph, and $k$ is a non-negative integer, then either $G$ contains $k$ vertex/edge-disjoint subgraphs, each containing $H$ as an immersion, or $G$ contains a set $F$ of $f(k,h)$ vertices/edges such that $G\\setminus F$ does not contain $H$ as an immersion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04042","kind":"arxiv","version":2},"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"}