In graph theory, an eternal dominating set for a graph G = (V, E) is a subset D of V such that D is a dominating set on which mobile guards are… (More)

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2018

2018

- Nathann Cohen, Nícolas A. Martins, Fionn Mc Inerney, Nicolas Nisse, Stéphane Pérennes, Rudini Menezes Sampaio
- Theor. Comput. Sci.
- 2018

We define and study the following two-player game on a graph G. Let k ∈ N∗. A set of k guards is occupying some vertices of G… (More)

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2017

2017

A vertex u of a graph “t-dominates” a vertex v if there are at most t vertices different from u, v that are adjacent to v and not… (More)

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2017

2017

- William Klostermeyer, Gary MacGillivray
- Discussiones Mathematicae Graph Theory
- 2017

We show that for every minimum eternal dominating set, D, of a graph G and every vertex v ∈ D, there is a sequence of attacks at… (More)

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2017

2017

In the Spy game, a spy is placed first at some vertex of a graph G. Then, k > 0 guards are also occupying some vertices of G. At… (More)

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2016

2016

We define and study the following two-player game on a graph G. Let k ∈ N∗. A set of k guards is occupying some vertices of G… (More)

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2015

2015

2015

- Stephen Finbow, Margaret-Ellen Messinger, Martin F. van Bommel
- Australasian J. Combinatorics
- 2015

In the eternal dominating set problem, guards form a dominating set on a graph and at each step, a vertex is attacked. After each… (More)

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2013

2013

During the last decades, many combinatorial games involving two persons playing on a (directed) graph have received a lot of… (More)

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