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