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Lower bounds for positive semidefinite zero forcing and their applications

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  • Boting Yang

    (University of Regina)

Abstract

The positive semidefinite zero forcing number of a graph is a parameter that is important in the study of minimum rank problems. In this paper, we focus on the algorithmic aspects of computing this parameter. We prove that it is NP-complete to find the positive semidefinite zero forcing number of a given graph, and this problem remains NP-complete even for graphs with maximum vertex degree 7. We present a linear time algorithm for computing the positive semidefinite zero forcing number of generalized series–parallel graphs. We introduce the constrained tree cover number and apply it to improve lower bounds for positive semidefinite zero forcing. We also give formulas for the constrained tree cover number and the tree cover number on graphs with special structures.

Suggested Citation

  • Boting Yang, 2017. "Lower bounds for positive semidefinite zero forcing and their applications," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 81-105, January.
    • Handle: RePEc:spr:jcomop:v:33:y:2017:i:1:d:10.1007_s10878-015-9936-0
    DOI: 10.1007/s10878-015-9936-0
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    References listed on IDEAS

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    1. Boting Yang, 2007. "Strong-mixed searching and pathwidth," Journal of Combinatorial Optimization, Springer, vol. 13(1), pages 47-59, January.
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    Cited by:

    1. Chassidy Bozeman & Boris Brimkov & Craig Erickson & Daniela Ferrero & Mary Flagg & Leslie Hogben, 2019. "Restricted power domination and zero forcing problems," Journal of Combinatorial Optimization, Springer, vol. 37(3), pages 935-956, April.

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