{"paper":{"title":"Graphlike families of multiweights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Agnese Baldisserri, Elena Rubei","submitted_at":"2016-06-29T17:03:51Z","abstract_excerpt":"Let ${\\cal G}=(G,w)$ be a weighted graph , that is, a graph $G$ endowed with a function $w$ from the edge set of $G$ to the set of real numbers; for any subset $S$ of the vertex set of $G$, we define $D_S({\\cal G})$ to be the minimum of the weights of the subgraphs of $G$ whose vertex set contains $S$; we call $D_S({\\cal G})$ a multiweight of ${\\cal G}$.\n  Let $X$ be a finite set and let $\\{D_S\\}_{S \\subset X, \\; \\sharp S \\geq 2} $ be a family of positive real numbers. We find necessary and sufficient conditions for the family to be the family of multiweights of a positive-weighted graph with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.09183","kind":"arxiv","version":3},"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"}