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The first gap for total curvatures of planar graphs with nonnegative curvature
Author(s) -
Hua Bobo,
Su Yanhui
Publication year - 2020
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22493
Subject(s) - mathematics , combinatorics , planar graph , planar , curvature , graph , outerplanar graph , metric (unit) , discrete mathematics , geometry , pathwidth , line graph , computer science , operations management , computer graphics (images) , economics
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.