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arXiv · 2402.10782

Finding forest-orderings of tournaments is NP-complete

Pierre Aboulker·Guillaume Aubian·Raul Lopes
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Abstract

Given a class of (undirected) graphs $\mathcal{C}$, we say that a Feedback Arc Set (FAS for short) $F$ is a $\mathcal{C}$-FAS if the graph induced by the edges of $F$ (forgetting their orientations) belongs to $\mathcal{C}$. We show that deciding if a tournament has a $\mathcal{C}$-FAS is NP-complete when $\mathcal{C}$ is the class of all forests. We are motivated by connections between $\mathcal{C}$-FAS and structural parameters of tournaments, such as the dichromatic number, the clique number of tournaments, and the strong Erd\H{o}s-Hajnal property.

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Pierre Aboulker, Guillaume Aubian, Raul Lopes. 2024-02-16. Finding forest-orderings of tournaments is NP-complete. https://doi.org/10.46298/dmtcs.14281

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