{"paper":{"title":"Algorithmic aspects of $M$-Lipschitz mappings of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Jan Bok","submitted_at":"2018-01-16T22:17:52Z","abstract_excerpt":"$M$-Lipschitz mappings of graphs (or equivalently graph-indexed random walks) are a generalization of standard random walk on $\\mathbb{Z}$. For $M \\in \\N$, an \\emph{$M$-Lipschitz mapping} of a connected rooted graph $G = (V,E)$ is a mapping $f: V \\to \\Z$ such that root is mapped to zero and for every edge $(u,v) \\in E$ we have $|f(u) - f(v)| \\le M$.\n  We study two natural problems regarding graph-indexed random walks. - Computing the maximum range of a graph-indexed random walk for a given graph. - Deciding if we can extend a partial GI random walk into a full GI random walk for a given graph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.05496","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"}