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Computing role assignments of split graphs.

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Title: Computing role assignments of split graphs.
Authors: Dourado, Mitre Costa1 mitre@dcc.ufrj.br
Source: Theoretical Computer Science. Jul2016, Vol. 635, p74-84. 11p.
Subjects: COMSKEE (Computer program language), Graphic methods, Student assignments, Social networks, Algorithms
Abstract: A k -role assignment of a simple graph G is a surjective function r : V ( G ) → { 1 , … , k } where { r ( u ′ ) : u ′ ∈ N ( u ) } = { r ( v ′ ) : v ′ ∈ N ( v ) } for every pair u , v ∈ V ( G ) with r ( u ) = r ( v ) . This concept appears in the context of social networks. It is known that the problem of finding a 2-role assignment of chordal graphs can be solved in linear time and that deciding whether a graph of this class admits a k -role assignment, for any fixed k ≥ 3 , is NP -complete. In this work, we investigate this problem on split graphs, a subclass of chordal graphs. We characterize the split graphs admitting a 3-role assignment. Such result leads to a linear time algorithm for this case. Furthermore, we prove that deciding whether a split graph has a k -role assignment is NP -complete for any fixed k ≥ 4 . [ABSTRACT FROM AUTHOR]
Copyright of Theoretical Computer Science 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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DbLabel: Engineering Source
An: 115677727
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  Data: <searchLink fieldCode="JN" term="%22Theoretical+Computer+Science%22">Theoretical Computer Science</searchLink>. Jul2016, Vol. 635, p74-84. 11p.
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  Data: <searchLink fieldCode="DE" term="%22COMSKEE+%28Computer+program+language%29%22">COMSKEE (Computer program language)</searchLink><br /><searchLink fieldCode="DE" term="%22Graphic+methods%22">Graphic methods</searchLink><br /><searchLink fieldCode="DE" term="%22Student+assignments%22">Student assignments</searchLink><br /><searchLink fieldCode="DE" term="%22Social+networks%22">Social networks</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink>
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  Data: A k -role assignment of a simple graph G is a surjective function r : V ( G ) → { 1 , … , k } where { r ( u ′ ) : u ′ ∈ N ( u ) } = { r ( v ′ ) : v ′ ∈ N ( v ) } for every pair u , v ∈ V ( G ) with r ( u ) = r ( v ) . This concept appears in the context of social networks. It is known that the problem of finding a 2-role assignment of chordal graphs can be solved in linear time and that deciding whether a graph of this class admits a k -role assignment, for any fixed k ≥ 3 , is NP -complete. In this work, we investigate this problem on split graphs, a subclass of chordal graphs. We characterize the split graphs admitting a 3-role assignment. Such result leads to a linear time algorithm for this case. Furthermore, we prove that deciding whether a split graph has a k -role assignment is NP -complete for any fixed k ≥ 4 . [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Theoretical Computer Science 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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      – Type: doi
        Value: 10.1016/j.tcs.2016.05.011
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      – Code: eng
        Text: English
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        PageCount: 11
        StartPage: 74
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      – SubjectFull: COMSKEE (Computer program language)
        Type: general
      – SubjectFull: Graphic methods
        Type: general
      – SubjectFull: Student assignments
        Type: general
      – SubjectFull: Social networks
        Type: general
      – SubjectFull: Algorithms
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      – TitleFull: Computing role assignments of split graphs.
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            NameFull: Dourado, Mitre Costa
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              Text: Jul2016
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              Y: 2016
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            – TitleFull: Theoretical Computer Science
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