{"paper":{"title":"Steiner trees and higher geodecity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel Wei{\\ss}auer","submitted_at":"2017-03-29T11:00:17Z","abstract_excerpt":"Let $G$ be a connected graph and $\\ell : E(G) \\to \\mathbb{R}^+$ a length-function on the edges of $G$. The Steiner distance $\\mathrm{sd}_G(A)$ of $A \\subseteq V(G)$ within $G$ is the minimum length of a connected subgraph of $G$ containing $A$, where the length of a subgraph is the sum of the lengths of its edges.\n  It is clear that every subgraph $H \\subseteq G$, with the induced length-function $\\ell|_{E(H)}$, satisfies $\\mathrm{sd}_H(A) \\geq \\mathrm{sd}_G(A)$ for every $A \\subseteq V(H)$. We call $H \\subseteq G$ $k$-geodesic in $G$ if equality is attained for every $A \\subseteq V(H)$ with $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09969","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"}