Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.author | 오병근 | - |
dc.date.accessioned | 2018-04-03T05:35:17Z | - |
dc.date.available | 2018-04-03T05:35:17Z | - |
dc.date.issued | 2014-06 | - |
dc.identifier.citation | DISCRETE & COMPUTATIONAL GEOMETRY; JUN 2014, 51 4, p859-p884, 26p. | en_US |
dc.identifier.issn | 0179-5376 | - |
dc.identifier.uri | http://link.springer.com/article/10.1007%2Fs00454-014-9592-7 | - |
dc.identifier.uri | http://hdl.handle.net/20.500.11754/56497 | - |
dc.description.abstract | This paper is about hyperbolic properties on planar graphs. First, we study the relations among various kinds of strong isoperimetric inequalities on planar graphs and their duals. In particular, we show that a planar graph satisfies a strong isoperimetric inequality if and only if its dual has the same property, if the graph satisfies some minor regularity conditions and we choose an appropriate notion of strong isoperimetric inequalities. Second, we consider planar graphs where negative combinatorial curvatures dominate, and use the outcomes of the first part to strengthen the results of Higuchi, A >> uk, and, especially, Woess. Finally, we study the relations between Gromov hyperbolicity and strong isoperimetric inequalities on planar graphs, and give a proof that a planar graph satisfying a proper kind of a strong isoperimetric inequality must be Gromov hyperbolic if face degrees of the graph are bounded. We also provide some examples to support our results. | en_US |
dc.description.sponsorship | The author appreciates Mario Bonk for helpful advices about Theorem 6(a), and KIAS (Korea Institute for Advanced Study) for its support through the Associate Member Program. This work was supported by the research fund of Hanyang University (HY-2009-N) and by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0004113). | en_US |
dc.language.iso | en | en_US |
dc.publisher | Springer Science + Business Media | en_US |
dc.subject | Isoperimetric inequality | en_US |
dc.subject | Planar graph | en_US |
dc.subject | Combinatorial curvature | en_US |
dc.subject | Gromov hyperbolicity | en_US |
dc.title | Duality Properties of Strong Isoperimetric Inequalities on a Planar Graph and Combinatorial Curvatures | en_US |
dc.type | Article | en_US |
dc.relation.no | 4 | - |
dc.relation.volume | 51 | - |
dc.identifier.doi | 10.1007/s00454-014-9592-7 | - |
dc.relation.page | 859-884 | - |
dc.relation.journal | DISCRETE & COMPUTATIONAL GEOMETRY | - |
dc.contributor.googleauthor | Oh, Byung-Geun | - |
dc.relation.code | 2014028435 | - |
dc.sector.campus | S | - |
dc.sector.daehak | COLLEGE OF EDUCATION[S] | - |
dc.sector.department | DEPARTMENT OF MATHEMATICS EDUCATION | - |
dc.identifier.pid | bgoh | - |
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