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arXiv · 2201.06577

Eternal vertex cover number of maximal outerplanar graphs

Jasine Babu·K. Murali Krishnan·Veena Prabhakaran·Nandini J. Warrier
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Abstract

Eternal vertex cover problem is a variant of the classical vertex cover problem modeled as a two player attacker-defender game. Computing eternal vertex cover number of graphs is known to be NP-hard in general and the complexity status of the problem for bipartite graphs is open. There is a quadratic complexity algorithm known for this problem for chordal graphs. Maximal outerplanar graphs forms a subclass of chordal graphs, for which no algorithm of sub-quadratic time complexity is known. In this paper, we obtain a recursive algorithm of linear time for computing eternal vertex cover number of maximal outerplanar graphs.

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Jasine Babu, K. Murali Krishnan, Veena Prabhakaran, Nandini J. Warrier. 2022-01-17. Eternal vertex cover number of maximal outerplanar graphs. https://arxiv.org/abs/2201.06577

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