FPT Isomorphism Test for $F$-Free Tournaments

2026-09-21

AI Summary

本文解决了F-自由锦标赛的同构问题，通过结合谱、几何、组合和群论工具，在固定参数时间内提供了一种新的解决方案。

Abstract

We show that isomorphism of $F$-free tournaments can be solved in FPT time $f(k) \cdot n^{O(1)}$, where $k$ denotes the size of $F$, and $n$ denotes the size of the input tournaments. Our result extends on a previous FPT isomorphism test for tournaments of bounded twin-width [Grohe, Neuen 2024], as well as XP isomorphism tests parameterized by the VC dimension or the chromatic number [Raßmann, Schweitzer 2026]. It also implies that every non-trivial hereditary class of tournaments admits a polynomial-time isomorphism test. Our algorithm builds on a novel combination of spectral, geometric, combinatorial and group-theoretic tools.

Problem

• FPT
• isomorphism test
• tournaments
• F-free

Innovation

• FPT isomorphism test
• spectral methods
• geometric tools
• combinatorial techniques
• group-theoretic tools