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arXiv · 2006.05464

The Max k-Cut Game: On Stable Optimal Colorings

Chiara Mocenni·Dario Madeo·Andrea Garuglieri·Simone Rinaldi·Giulia Palma
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Abstract

We study the max k-cut game on an undirected and unweighted graph in order to find out whether an optimal solution is also a strong equilibrium. While we do fail to show that, by proving an alternate formula for computing the cut value difference for a strong deviation, we show that optimal solutions are 7-stable equilibria. Furthermore, we prove some properties of minimal subsets with respect to a strong deviation, showing that each of their nodes will deviate towards the color of one of their neighbors and that those subsets induce connected subgraphs.

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Chiara Mocenni, Dario Madeo, Andrea Garuglieri, Simone Rinaldi, Giulia Palma. 2020-06-09. The Max k-Cut Game: On Stable Optimal Colorings. https://arxiv.org/abs/2006.05464

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