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On the number of vertices of positively curved planar graphs

Title
On the number of vertices of positively curved planar graphs
Author
오병근
Keywords
Planar graph; Combinatorial curvature; Discharging method
Issue Date
2017-06
Publisher
ELSEVIER SCIENCE BV
Citation
DISCRETE MATHEMATICS, v. 340, no. 6, page. 1300-1310
Abstract
For a connected simple graph embedded into a 2-sphere, we show that the number of vertices of the graph is less than or equal to 380 if the degree of each vertex is at least three, the combinatorial vertex curvature is positive everywhere, and the graph is different from prisms and antiprisms. This gives a new upper bound for the constant brought up by DeVos and Mohar in their paper from 2007. We also show that if a graph is embedded into a projective plane instead of a 2-sphere but satisfies the other properties listed above, then the number of vertices is at most 190. (C) 2017 Elsevier B.V. All rights reserved.
URI
https://www.sciencedirect.com/science/article/abs/pii/S0012365X17300353?via%3Dihubhttps://repository.hanyang.ac.kr/handle/20.500.11754/114509
ISSN
0012-365X; 1872-681X
DOI
10.1016/j.disc.2017.01.025
Appears in Collections:
COLLEGE OF EDUCATION[S](사범대학) > MATHEMATICS EDUCATION(수학교육과) > Articles
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