{"paper":{"title":"From G-parking functions to B-parking functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fengming Dong","submitted_at":"2014-07-08T08:04:08Z","abstract_excerpt":"A matching $M$ in a multigraph $G=(V,E)$ is said to be uniquely restricted if $M$ is the only perfect matching in the subgraph of $G$ induced by $V(M)$ (i.e., the set of vertices saturated by $M$). For any fixed vertex $x_0$ in $G$, there is a bijection from the set of spanning trees of $G$ to the set of uniquely restricted matchings of size $|V|-1$ in $S(G)-x_0$, where $S(G)$ is the bipartite graph obtained from $G$ by subdividing each edge in $G$. Thus the notion \"uniquely restricted matchings of a bipartite graph $H$ saturating all vertices in a partite set $X$\" can be viewed as an extensio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1983","kind":"arxiv","version":6},"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"}