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We prove that the total curvature of a planar graph with nonnegative combinatorial curvature is at least 1/12 if it is positive. Moreover, we classify the metric structures of ambient polygonal surfaces for planar graphs attaining this bound. © 2019 Wiley Periodicals, Inc.
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Journal of Graph Theory
ISSN: 0364-9024
Year: 2020
Issue: 3
Volume: 93
Page: 395-439
0 . 8 5 7
JCR@2020
0 . 9 0 0
JCR@2023
ESI HC Threshold:50
JCR Journal Grade:3
CAS Journal Grade:3
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