dc.contributor.author | Price, Gregory N. | |
dc.contributor.author | Lee, James R. | |
dc.contributor.author | Teng, Shang-Hua | |
dc.contributor.author | Kelner, Jonathan Adam | |
dc.date.accessioned | 2010-10-21T14:32:29Z | |
dc.date.available | 2010-10-21T14:32:29Z | |
dc.date.issued | 2010-03 | |
dc.date.submitted | 2009-10 | |
dc.identifier.isbn | 978-1-4244-5116-6 | |
dc.identifier.issn | 0272-5428 | |
dc.identifier.other | INSPEC Accession Number: 11207105 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/59440 | |
dc.description.abstract | We present a general method for proving upper bounds on the eigenvalues of the graph Laplacian. In particular, we show that for any positive integer k, the kth smallest eigenvalue of the Laplacian on a bounded-degree planar graph is O(k/n). This bound is asymptotically tight for every k, as it is easily seen to be achieved for planar grids. We also extend this spectral result to graphs with bounded genus, graphs which forbid fixed minors, and other natural families. Previously, such spectral upper bounds were only known for k = 2, i.e. for the Fiedler value of these graphs. In addition, our result yields a new, combinatorial proof of the celebrated result of Korevaar in differential geometry. | en_US |
dc.description.sponsorship | National Science Foundation (U.S.) (CCF-0843915) | en_US |
dc.description.sponsorship | National Science Foundation (U.S.) (CCF-0644037) | en_US |
dc.description.sponsorship | National Science Foundation (U.S.) (CCF-0635102) | en_US |
dc.description.sponsorship | Akamai Technologies, Inc. | en_US |
dc.description.sponsorship | National Science Foundation (U.S.). Graduate Research Fellowship Program | en_US |
dc.language.iso | en_US | |
dc.publisher | Institute of Electrical and Electronics Engineers | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1109/FOCS.2009.69 | en_US |
dc.rights | Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. | en_US |
dc.source | IEEE | en_US |
dc.title | Higher eigenvalues of graphs | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Kelner, J.A. et al. “Higher Eigenvalues of Graphs.” Foundations of Computer Science, 2009. FOCS '09. 50th Annual IEEE Symposium on. 2009. 735-744. ©2009 Institute of Electrical and Electronics Engineers. | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | en_US |
dc.contributor.approver | Kelner, Jonathan Adam | |
dc.contributor.mitauthor | Price, Gregory N. | |
dc.contributor.mitauthor | Kelner, Jonathan Adam | |
dc.relation.journal | 50th Annual IEEE Symposium on Foundations of Computer Science, 2009. FOCS '09 | en_US |
dc.eprint.version | Final published version | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dspace.orderedauthors | Kelner, Jonathan A.; Lee, James R.; Price, Gregory N.; Teng, Shang-Hua | en |
dc.identifier.orcid | https://orcid.org/0000-0002-4257-4198 | |
mit.license | PUBLISHER_POLICY | en_US |
mit.metadata.status | Complete | |