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On graphs with minimal eternal vertex cover number

Babu, J and Chandran, LS and Francis, M and Prabhakaran, V and Rajendraprasad, D and Warrier, JN (2019) On graphs with minimal eternal vertex cover number. In: 5th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2019, 14 - 16 February 2019, Kharagpur, pp. 263-273.

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Official URL: https://doi.org/10.1007/978-3-030-11509-8_22


The eternal vertex cover problem is a variant of the classical vertex cover problem where a set of guards on the vertices have to be dynamically reconfigured from one vertex cover to another in every round of an attacker-defender game. The minimum number of guards required to protect a graph from an infinite sequence of attacks is the eternal vertex cover number (evc) of the graph. It is known that, given a graph G and an integer k, checking whether (G)≤k is NP-Hard. However, for any graph G, (Formula presentd), where mvc(G) is the minimum vertex cover number of G. Precise value of eternal vertex cover number is known only for certain very basic graph classes like trees, cycles and grids. Though a characterization is known for graphs for which evc(G) = 2 mvc(G), a characterization of graphs for which evc(G) = mvc(G) remained open. Here, we achieve such a characterization for a class of graphs that includes chordal graphs and internally triangulated planar graphs. For some graph classes including biconnected chordal graphs, our characterization leads to a polynomial time algorithm to precisely determine evc(G) and to determine a safe strategy of guard movement in each round of the game with evc(G) guards.

Item Type: Conference Paper
Publication: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Publisher: Springer Verlag
Additional Information: The copyright for this article belongs to Springer Verlag.
Keywords: Graphic methods; Polynomial approximation; Trees (mathematics), Basic graphs; Chordal graphs; Connected vertex cover; Minimum vertex cover; Planar graph; Polynomial-time algorithms; Vertex cover; Vertex Cover problems, Graph theory
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Date Deposited: 18 Nov 2022 09:27
Last Modified: 18 Nov 2022 09:27
URI: https://eprints.iisc.ac.in/id/eprint/77990

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