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arXiv · 2306.15206

A characterization of graphs of radius-$r$ flip-width at most $2$

Yeonsu Chang·Sejin Ko·O-joung Kwon·Myounghwan Lee
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Abstract

The $r$-flip-width of a graph, for $r\in \mathbb{N}\cup \{\infty\}$, is a graph parameter defined in terms of a variant of the cops and robber game, called the flipper game, and it was introduced by Toruńczyk (FOCS 2023). We prove that for every $r\in (\mathbb{N}\setminus \{1\})\cup \{\infty\}$, the class of graphs of $r$-flip-width at most $2$ is exactly the class of ($C_5$, bull, gem, co-gem)-free graphs, which are known as totally decomposable graphs with respect to bi-joins.

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Yeonsu Chang, Sejin Ko, O-joung Kwon, Myounghwan Lee. 2024-10-19. A characterization of graphs of radius-$r$ flip-width at most $2$. https://arxiv.org/abs/2306.15206

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