{"paper":{"title":"Hadwiger's conjecture for $\\ell$-link graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bin Jia, David R. Wood","submitted_at":"2014-02-28T13:15:31Z","abstract_excerpt":"In this paper we define and study a new family of graphs that generalises the notions of line graphs and path graphs. Let $G$ be a graph with no loops but possibly with parallel edges. An \\emph{$\\ell$-link} of $G$ is a walk of $G$ of length $\\ell \\geqslant 0$ in which consecutive edges are different. We identify an $\\ell$-link with its reverse sequence. The \\emph{$\\ell$-link graph $\\mathbb{L}_\\ell(G)$} of $G$ is the graph with vertices the $\\ell$-links of $G$, such that two vertices are joined by $\\mu \\geqslant 0$ edges in $\\mathbb{L}_\\ell(G)$ if they correspond to two subsequences of each of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.7235","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"}