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<p>We prove that for any finite tournament and any of its partial automorphisms there exists a finite extension of the original tournament in which this partial automorphism can be extended to a complete automorphism. An estimate for the size of this extension is given. Furthermore, it is proved that every finite tournament has a finite transitive extension, and the order of this extension is specified.</p>

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Extension of Partial Automorphisms in Finite Tournament

  • 期刊论文

  • 发表日期：

    2025年7月1日

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  • K. Zh. Kudaibergenov

摘要

We prove that for any finite tournament and any of its partial automorphisms there exists a finite extension of the original tournament in which this partial automorphism can be extended to a complete automorphism. An estimate for the size of this extension is given. Furthermore, it is proved that every finite tournament has a finite transitive extension, and the order of this extension is specified.