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Exact and approximate results on the least size of a graph with a given degree set.

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Title: Exact and approximate results on the least size of a graph with a given degree set.
Authors: Moondra, Jai1 (AUTHOR) jmoondra3@gatech.edu, Sahdev, Aditya1,2 (AUTHOR) aditya.sahdev@alumni.iitd.ac.in, Tripathi, Amitabha1,3 (AUTHOR) atripath@maths.iitd.ac.in
Source: Discrete Applied Mathematics. Jul2023, Vol. 333, p32-42. 11p.
Abstract: The degree set of a finite simple graph G is the set of distinct degrees of vertices of G. A theorem of Kapoor, Polimeni & Wall asserts that the least order of a graph with a given degree set D is 1 + max D. Tripathi & Vijay considered the analogous problem concerning the least size of graphs with degree set D. We expand on their results, and determine the least size of graphs with degree set D when (i) min D divides d for each d ∈ D ; (ii) min D = 2 ; (iii) D = { m , m + 1 , ... , n }. In addition, given any D , we produce a graph G whose size is within min D of the optimal size, giving a (1 + 2 d 1 + 1) -approximation, where d 1 = max D. [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.)
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  Data: Exact and approximate results on the least size of a graph with a given degree set.
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  Data: <searchLink fieldCode="AR" term="%22Moondra%2C+Jai%22">Moondra, Jai</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jmoondra3@gatech.edu</i><br /><searchLink fieldCode="AR" term="%22Sahdev%2C+Aditya%22">Sahdev, Aditya</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> aditya.sahdev@alumni.iitd.ac.in</i><br /><searchLink fieldCode="AR" term="%22Tripathi%2C+Amitabha%22">Tripathi, Amitabha</searchLink><relatesTo>1,3</relatesTo> (AUTHOR)<i> atripath@maths.iitd.ac.in</i>
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  Data: <searchLink fieldCode="JN" term="%22Discrete+Applied+Mathematics%22">Discrete Applied Mathematics</searchLink>. Jul2023, Vol. 333, p32-42. 11p.
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  Data: The degree set of a finite simple graph G is the set of distinct degrees of vertices of G. A theorem of Kapoor, Polimeni & Wall asserts that the least order of a graph with a given degree set D is 1 + max D. Tripathi & Vijay considered the analogous problem concerning the least size of graphs with degree set D. We expand on their results, and determine the least size of graphs with degree set D when (i) min D divides d for each d ∈ D ; (ii) min D = 2 ; (iii) D = { m , m + 1 , ... , n }. In addition, given any D , we produce a graph G whose size is within min D of the optimal size, giving a (1 + 2 d 1 + 1) -approximation, where d 1 = max D. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  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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      – Type: doi
        Value: 10.1016/j.dam.2023.02.012
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      – Code: eng
        Text: English
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        PageCount: 11
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      – TitleFull: Exact and approximate results on the least size of a graph with a given degree set.
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            NameFull: Moondra, Jai
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            NameFull: Sahdev, Aditya
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            NameFull: Tripathi, Amitabha
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            – D: 15
              M: 07
              Text: Jul2023
              Type: published
              Y: 2023
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              Value: 333
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