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The Complexity of the Positive Semidefinite Zero Forcing

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Combinatorial Optimization and Applications (COCOA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8881))

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Abstract

The positive zero forcing number of a graph is a graph parameter that arises from a non-traditional type of graph colouring, and is related to a more conventional version of zero forcing. We establish a relation between the zero forcing and the fast-mixed searching, which implies some NP-completeness results for the zero forcing problem. For chordal graphs much is understood regarding the relationships between positive zero forcing and clique coverings. Building upon constructions associated with optimal tree covers and forest covers, we present a linear time algorithm for computing the positive zero forcing number of chordal graphs. We also prove that it is NP-complete to determine if a graph has a positive zero forcing set with an additional property.

Shaun Fallat: Research supported in part by an NSERC Discovery Research Grant, Application No.: RGPIN-2014-06036.

Karen Meagher: Research supported in part by an NSERC Discovery Research Grant, Application No.: RGPIN-341214-2013.

Boting Yang: Research supported in part by an NSERC Discovery Research Grant, Application No.: RGPIN-2013-261290.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Regina, Regina, Canada

    Shaun Fallat & Karen Meagher

  2. Department of Computer Science, University of Regina, Regina, Canada

    Boting Yang

Authors
  1. Shaun Fallat
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  2. Karen Meagher
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  3. Boting Yang
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Corresponding author

Correspondence to Boting Yang .

Editor information

Editors and Affiliations

  1. Zhejiang Normal University, Jinhua, Zhejiang, China

    Zhao Zhang

  2. University of Texas, Tyler, Texas, USA

    Lidong Wu

  3. University of Texas, Dallas, Texas, USA

    Wen Xu

  4. University of Texas, Dallas, USA

    Ding-Zhu Du

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© 2014 Springer International Publishing Switzerland

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Fallat, S., Meagher, K., Yang, B. (2014). The Complexity of the Positive Semidefinite Zero Forcing. In: Zhang, Z., Wu, L., Xu, W., Du, DZ. (eds) Combinatorial Optimization and Applications. COCOA 2014. Lecture Notes in Computer Science(), vol 8881. Springer, Cham. https://doi.org/10.1007/978-3-319-12691-3_51

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  • DOI: https://doi.org/10.1007/978-3-319-12691-3_51

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12690-6

  • Online ISBN: 978-3-319-12691-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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