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Note on the bisection width of cubic graphs.

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Title: Note on the bisection width of cubic graphs.
Authors: Jobson, Adam S.1 (AUTHOR) adam.jobson@louisville.edu, Kézdy, André E.1 (AUTHOR) andre.kezdy@louisville.edu, Lehel, Jenő1,2 (AUTHOR) lehelj@renyi.hu
Source: Discrete Applied Mathematics. Oct2020, Vol. 285, p434-442. 9p.
Subjects: Parallel processing
Abstract: The bisection width is the minimum number of edges required to split the vertex set of a graph into two (nearly) equal parts. Monien and Preis proved that the bisection width of a cubic graph with n nodes is bounded above by n ∕ 6 + o (n). Here we show that every cubic graph of even order n ≥ 16 has bisection width less than n ∕ 2 , thus these graphs violate the even cut condition (ECC). All edge-minimal subcubic graphs satisfying ECC are also described. The bisection width is a reference parameter to compare networks for parallel architectures; ECC is a property necessary for bottleneck free all-to-all communications. [ABSTRACT FROM AUTHOR]
Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 145407645
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PubType: Academic Journal
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  Data: The bisection width is the minimum number of edges required to split the vertex set of a graph into two (nearly) equal parts. Monien and Preis proved that the bisection width of a cubic graph with n nodes is bounded above by n ∕ 6 + o (n). Here we show that every cubic graph of even order n ≥ 16 has bisection width less than n ∕ 2 , thus these graphs violate the even cut condition (ECC). All edge-minimal subcubic graphs satisfying ECC are also described. The bisection width is a reference parameter to compare networks for parallel architectures; ECC is a property necessary for bottleneck free all-to-all communications. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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        Value: 10.1016/j.dam.2020.06.017
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      – Code: eng
        Text: English
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        PageCount: 9
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      – TitleFull: Note on the bisection width of cubic graphs.
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              Text: Oct2020
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