Cheeger's cut, maxcut and the spectral theory of1-Laplacian on graphs

被引：0

作者：

CHANG KungChing ^{[1
]}

SHAO SiHong ^{[1
]}

ZHANG Dong ^{[1
]}

机构：

[1] LMAM and School of Mathematical Sciences, Peking University

来源：

Science China Mathematics | 2017年 / 60卷 / 11期

基金：

中国国家自然科学基金;

关键词：

spectral graph theory; Laplacian; graph cut; optimization; critical point theory;

D O I：

暂无

中图分类号：

O157.5 [图论];

学科分类号：

070104 ;

摘要：

This is primarily an expository paper surveying up-to-date known results on the spectral theory of1-Laplacian on graphs and its applications to the Cheeger cut, maxcut and multi-cut problems. The structure of eigenspace, nodal domains, multiplicities of eigenvalues, and algorithms for graph cuts are collected.

引用

页码：1963 / 1980

页数：18

共 30 条

[1] Cheeger's cut, maxcut and the spectral theory of 1-Laplacian on graphs
Chang, KungChing
Shao, SiHong
Zhang, Dong
SCIENCE CHINA-MATHEMATICS, 2017, 60 (11) : 1963 - 1980
[2] Cheeger’s cut, maxcut and the spectral theory of 1-Laplacian on graphs
KungChing Chang
SiHong Shao
Dong Zhang
Science China Mathematics, 2017, 60 : 1963 - 1980
[3] THE 1-LAPLACIAN CHEEGER CUT: THEORY AND ALGORITHMS
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JOURNAL OF COMPUTATIONAL MATHEMATICS, 2015, 33 (05): : 443 - 467
[4] Spectrum of the 1-Laplacian and Cheeger's Constant on Graphs
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[5] Finding Cheeger Cuts via 1-Laplacian of Graphs
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[6] On the signless Laplacian spectral radius of graphs with cut vertices
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[7] The First Two Largest Eigenvalues of Laplacian, Spectral Gap Problem and Cheeger Constant of Graphs
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[8] The spectral radius of submatrices of Laplacian matrices for graphs with cut vertices
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LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 428 (8-9) : 1987 - 1999
[9] Some results on Laplacian spectral radius of graphs with cut vertices
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[10] On the distance and distance Laplacian spectral radius of graphs with cut edges
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