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Parameterized complexity of graph planarity with restricted cyclic orders.

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Title: Parameterized complexity of graph planarity with restricted cyclic orders.
Authors: Liotta, Giuseppe1 (AUTHOR) giuseppe.liotta@unipg.it, Rutter, Ignaz2 (AUTHOR) rutter@fim.uni-passau.de, Tappini, Alessandra1 (AUTHOR) alessandra.tappini@unipg.it
Source: Journal of Computer & System Sciences. Aug2023, Vol. 135, p125-144. 20p.
Subjects: Representations of graphs, Planar graphs, Graph algorithms
Abstract: We study the complexity of testing whether a biconnected graph G = (V , E) is planar with the constraint that some cyclic orders of the edges incident to its vertices are allowed while some others are forbidden. The allowed cyclic orders are described by associating every vertex v of G with a set D (v) of FPQ-trees. Let tw be the treewidth of G and let D max be the maximum number of FPQ-trees per vertex. We show that the problem is FPT when parameterized by tw + D max , paraNP-hard when parameterized by D max , and W[1]-hard when parameterized by tw. We also consider NodeTrix planar representations of clustered graphs, where clusters are adjacency matrices and inter-cluster edges are non-intersecting simple curves. We prove that NodeTrix planarity with fixed sides is FPT when parameterized by the size of clusters plus the treewidth of the graph obtained by collapsing clusters to single vertices, provided that this graph is biconnected. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Computer & System Sciences is the property of Academic Press Inc. 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: Parameterized complexity of graph planarity with restricted cyclic orders.
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  Data: <searchLink fieldCode="AR" term="%22Liotta%2C+Giuseppe%22">Liotta, Giuseppe</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> giuseppe.liotta@unipg.it</i><br /><searchLink fieldCode="AR" term="%22Rutter%2C+Ignaz%22">Rutter, Ignaz</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> rutter@fim.uni-passau.de</i><br /><searchLink fieldCode="AR" term="%22Tappini%2C+Alessandra%22">Tappini, Alessandra</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> alessandra.tappini@unipg.it</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Computer+%26+System+Sciences%22">Journal of Computer & System Sciences</searchLink>. Aug2023, Vol. 135, p125-144. 20p.
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  Data: <searchLink fieldCode="DE" term="%22Representations+of+graphs%22">Representations of graphs</searchLink><br /><searchLink fieldCode="DE" term="%22Planar+graphs%22">Planar graphs</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+algorithms%22">Graph algorithms</searchLink>
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  Data: We study the complexity of testing whether a biconnected graph G = (V , E) is planar with the constraint that some cyclic orders of the edges incident to its vertices are allowed while some others are forbidden. The allowed cyclic orders are described by associating every vertex v of G with a set D (v) of FPQ-trees. Let tw be the treewidth of G and let D max be the maximum number of FPQ-trees per vertex. We show that the problem is FPT when parameterized by tw + D max , paraNP-hard when parameterized by D max , and W[1]-hard when parameterized by tw. We also consider NodeTrix planar representations of clustered graphs, where clusters are adjacency matrices and inter-cluster edges are non-intersecting simple curves. We prove that NodeTrix planarity with fixed sides is FPT when parameterized by the size of clusters plus the treewidth of the graph obtained by collapsing clusters to single vertices, provided that this graph is biconnected. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Computer & System Sciences is the property of Academic Press Inc. 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.jcss.2023.02.007
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 20
        StartPage: 125
    Subjects:
      – SubjectFull: Representations of graphs
        Type: general
      – SubjectFull: Planar graphs
        Type: general
      – SubjectFull: Graph algorithms
        Type: general
    Titles:
      – TitleFull: Parameterized complexity of graph planarity with restricted cyclic orders.
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            NameFull: Liotta, Giuseppe
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            NameFull: Rutter, Ignaz
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            NameFull: Tappini, Alessandra
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            – D: 01
              M: 08
              Text: Aug2023
              Type: published
              Y: 2023
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              Value: 135
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            – TitleFull: Journal of Computer & System Sciences
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