Local 2-separators

Johannes Carmesin

doi:10.1016/j.jctb.2022.04.005

Local 2-separators

Johannes Carmesin

Mathematics

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Abstract

How can sparse graph theory be extended to large networks, where algorithms whose running time is estimated using the number of vertices are not good enough? I address this question by introducing ‘Local Separators’ of graphs. Applications include:

1. A unique decomposition theorem for graphs along their local 2-separators analogous to the 2-separator theorem;
2. an exact characterisation of graphs with no bounded subdivision of a wheel [9].

Original language	English
Pages (from-to)	101-144
Number of pages	44
Journal	Journal of Combinatorial Theory. Series B
Volume	156
Early online date	10 May 2022
DOIs	https://doi.org/10.1016/j.jctb.2022.04.005
Publication status	Published - Sept 2022

Bibliographical note

Publisher Copyright:
© 2022

Keywords

Characterisations of graphs
2-separator theorem
Locality
Local cutvertices
Local separators
Structural graph theory

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10.1016/j.jctb.2022.04.005

CarmesinJ2022LocalAccepted author manuscript, 468 KBLicence: Creative Commons: Attribution-NonCommercial-NoDerivs (CC BY-NC-ND)

Cite this

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title = "Local 2-separators",

abstract = "How can sparse graph theory be extended to large networks, where algorithms whose running time is estimated using the number of vertices are not good enough? I address this question by introducing {\textquoteleft}Local Separators{\textquoteright} of graphs. Applications include:1. A unique decomposition theorem for graphs along their local 2-separators analogous to the 2-separator theorem;2. an exact characterisation of graphs with no bounded subdivision of a wheel [9].",

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KW - Characterisations of graphs

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KW - Locality

KW - Local cutvertices

KW - Local separators

KW - Structural graph theory

UR - https://arxiv.org/abs/2008.03032

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JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

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Local 2-separators

Abstract

Bibliographical note

Keywords

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