{"paper":{"title":"A Generalized Cheeger Inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Gary Miller, Ioannis Koutis, Richard Peng","submitted_at":"2014-10-22T15:48:54Z","abstract_excerpt":"The generalized conductance $\\phi(G,H)$ between two graphs $G$ and $H$ on the same vertex set $V$ is defined as the ratio $$\n  \\phi(G,H) = \\min_{S\\subseteq V} \\frac{cap_G(S,\\bar{S})}{ cap_H(S,\\bar{S})}, $$ where $cap_G(S,\\bar{S})$ is the total weight of the edges crossing from $S$ to $\\bar{S}=V-S$. We show that the minimum generalized eigenvalue $\\lambda(L_G,L_H)$ of the pair of Laplacians $L_G$ and $L_H$ satisfies $$\n  \\lambda(L_G,L_H) \\geq \\phi(G,H) \\phi(G)/8, $$ where $\\phi(G)$ is the usual conductance of $G$. A generalized cut that meets this bound can be obtained from the generalized eige"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6075","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"}