{"paper":{"title":"A Linear Cheeger Inequality using Eigenvector Norms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Franklin H. J. Kenter","submitted_at":"2014-12-10T04:33:32Z","abstract_excerpt":"The Cheeger constant, $h_G$, is a measure of expansion within a graph. The classical Cheeger Inequality states: $\\lambda_{1}/2 \\le h_G \\le \\sqrt{2 \\lambda_{1}}$ where $\\lambda_1$ is the first nontrivial eigenvalue of the normalized Laplacian matrix. Hence, $h_G$ is tightly controlled by $\\lambda_1$ to within a quadratic factor.\n  We give an alternative Cheeger Inequality where we consider the $\\infty$-norm of the corresponding eigenvector in addition to $\\lambda_1$. This inequality controls $h_G$ to within a linear factor of $\\lambda_1$ thereby providing an improvement to the previous quadrati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3195","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"}