{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:54Z","timestamp":1753893834347,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We derive upper and lower bounds on the isoperimetric numbers and bisection widths of a large class of regular graphs of high degree. Our methods are combinatorial and do not require a knowledge of the eigenvalue spectrum.   We apply these bounds to random regular graphs of high degree and the Platonic graphs over the rings $\\mathbb{Z}_n$.  In the latter case we show that these graphs are generally non-Ramanujan for composite $n$ and we also give sharp asymptotic bounds for the isoperimetric numbers.  We conclude by giving bounds on the Cheeger constants of arithmetic Riemann surfaces. For a large class of these surfaces these bounds are an improvement over the known asymptotic bounds.<\/jats:p>","DOI":"10.37236\/651","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:43:10Z","timestamp":1578714190000},"source":"Crossref","is-referenced-by-count":1,"title":["Isoperimetric Numbers of Regular Graphs of High Degree with Applications to Arithmetic Riemann Surfaces"],"prefix":"10.37236","volume":"18","author":[{"given":"Dominic","family":"Lanphier","sequence":"first","affiliation":[]},{"given":"Jason","family":"Rosenhouse","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2011,8,12]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p164\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p164\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:07:12Z","timestamp":1579302432000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p164"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,8,12]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/651","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,8,12]]},"article-number":"P164"}}