{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:17Z","timestamp":1753893857388,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We prove a theorem that can be thought of as a common generalization of the Discrete Nodal Theorem and (one direction of) Cheeger's Inequality for graphs. A special case of this result will assert that if the second and third eigenvalues of the Laplacian are at least $\\varepsilon$ apart, then the subgraphs induced by the positive and negative supports of the eigenvector belonging to $\\lambda_2$ are not only connected, but edge-expanders (in a weighted sense, with expansion depending on $\\varepsilon$).<\/jats:p>","DOI":"10.37236\/9944","type":"journal-article","created":{"date-parts":[[2021,9,23]],"date-time":"2021-09-23T10:50:17Z","timestamp":1632394217000},"source":"Crossref","is-referenced-by-count":1,"title":["Discrete Quantitative Nodal Theorem"],"prefix":"10.37236","volume":"28","author":[{"given":"L\u00e1szl\u00f3","family":"Lov\u00e1sz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2021,9,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i3p58\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i3p58\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,23]],"date-time":"2021-09-23T10:50:18Z","timestamp":1632394218000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i3p58"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,24]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,7,1]]}},"URL":"https:\/\/doi.org\/10.37236\/9944","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2021,9,24]]},"article-number":"P3.58"}}