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A New Lower Bound for the Eternal Vertex Cover Number of Graphs

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 12273)

Abstract

We obtain a new lower bound for the eternal vertex cover number of an arbitrary graph G, in terms of the cardinality of a vertex cover of minimum size in G containing all its cut vertices. The consequences of the lower bound include a quadratic time algorithm for computing the eternal vertex cover number of chordal graphs.

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Notes

  1. 1.

    The results in Fomin et al.  [6] are given for the variant of the problem in which more than one guard is allowed to be on a vertex in a configuration. But, the proof can be easily modified for to work for the other model as well.

  2. 2.

    Note that the definition of this graph class is more general than the one in [2].

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Correspondence to Jasine Babu .

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Babu, J., Prabhakaran, V. (2020). A New Lower Bound for the Eternal Vertex Cover Number of Graphs. In: Kim, D., Uma, R., Cai, Z., Lee, D. (eds) Computing and Combinatorics. COCOON 2020. Lecture Notes in Computer Science(), vol 12273. Springer, Cham. https://doi.org/10.1007/978-3-030-58150-3_3

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  • DOI: https://doi.org/10.1007/978-3-030-58150-3_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-58149-7

  • Online ISBN: 978-3-030-58150-3

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