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arXiv · 2309.05297

On Ahn-Hendrey-Kim-Oum question for twin-width of graphs with 6 vertices

Kajal Das
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Abstract

Twin-width is a recently introduced graph parameter for finite graphs. It is an open problem to determine whether there is an $n$-vertex graph having twin-width at least $n/2$ (due to J. Ahn, K. Hendrey, D. Kim and S. Oum). In an earlier paper, the author showed that such a graph with less than equal to 5 vertices does not exist. In this article, we show that such a graph with 6 vertices does not exist. More precisely, we prove that each graph with 6 vertices has twin-width less than equal to 2.

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Kajal Das. 2023-09-11. On Ahn-Hendrey-Kim-Oum question for twin-width of graphs with 6 vertices. https://arxiv.org/abs/2309.05297

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