{"paper":{"title":"Count Matroids of Group-Labeled Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Rintaro Ikeshita, Shin-ichi Tanigawa","submitted_at":"2015-07-05T19:12:30Z","abstract_excerpt":"A graph $G=(V,E)$ is called $(k,\\ell)$-sparse if $|F|\\leq k|V(F)|-\\ell$ for any nonempty $F\\subseteq E$, where $V(F)$ denotes the set of vertices incident to $F$. It is known that the family of the edge sets of $(k,\\ell)$-sparse subgraphs forms the family of independent sets of a matroid, called the $(k,\\ell)$-count matroid of $G$. In this paper we shall investigate lifts of the $(k,\\ell)$-count matroid by using group labelings on the edge set. By introducing a new notion called near-balancedness, we shall identify a new class of matroids, where the independence condition is described as a cou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01259","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"}