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arXiv · 2501.00991

Twin-width one

Jungho Ahn·Hugo Jacob·Noleen Köhler·Christophe Paul·Amadeus Reinald·Sebastian Wiederrecht
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Abstract

We investigate the structure of graphs of twin-width at most $1$, and obtain the following results: - Graphs of twin-width at most $1$ are permutation graphs. In particular they have an intersection model and a linear structure. - There is always a $1$-contraction sequence closely following a given permutation diagram. - Based on a recursive decomposition theorem, we obtain a simple algorithm running in linear time that produces a $1$-contraction sequence of a graph, or guarantees that it has twin-width more than $1$. - We characterise distance-hereditary graphs based on their twin-width and deduce a linear time algorithm to compute optimal sequences on this class of graphs.

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Jungho Ahn, Hugo Jacob, Noleen Köhler, Christophe Paul, Amadeus Reinald, Sebastian Wiederrecht. 2025-01-02. Twin-width one. https://arxiv.org/abs/2501.00991

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