Strong Isoperimetric Inequalities and Combinatorial Curvatures on Multiply Connected Planar Graphs

Title
Strong Isoperimetric Inequalities and Combinatorial Curvatures on Multiply Connected Planar Graphs
Author
오병근
Keywords
Strong isoperimetric inequality; Multiply connected planar graph; Combinatorial curvature
Issue Date
2016-10
Publisher
SPRINGER
Citation
DISCRETE & COMPUTATIONAL GEOMETRY, v. 56, NO 3, Page. 558-591
Abstract
The main focus of this paper is on hyperbolic properties of multiply connected planar graphs (planar graphs with multiple ends), and in the course we study some problematic phenomena of planar graphs caused by the existence of multiple (or sometimes infinite) ends. Specifically, in the first part of the paper we examine strong isoperimetric inequalities on a multiply connected planar graph G and its dual graph , and prove that G satisfies a strong isoperimetric inequality if and only if has the same property, provided that G is either normal or finitely connected and we choose an appropriate notion for strong isoperimetric inequalities. In the second part we study a planar graph G on which negative curvatures uniformly dominate positive curvatures, and give a criterion that guarantees a strong isoperimetric inequality on G. Our criterion is useful in that it can be applied to a graph containing a long and slim subgraph with nonnegative combinatorial curvatures.
URI
https://link.springer.com/article/10.1007%2Fs00454-016-9805-3http://repository.hanyang.ac.kr/handle/20.500.11754/100542
ISSN
0179-5376; 1432-0444
DOI
10.1007/s00454-016-9805-3
Appears in Collections:
COLLEGE OF EDUCATION[S](사범대학) > MATHEMATICS EDUCATION(수학교육과) > Articles
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