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<p>We prove that there exists a constant <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="493_2025_161_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">\(c &gt; 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>c</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> such that the vertices of every strongly <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="493_2025_161_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">\(c \cdot kt\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>c</mi> <mo>·</mo> <mi>k</mi> <mi>t</mi> </mrow> </math></EquationSource> </InlineEquation>-connected tournament can be partitioned into <i>t</i> parts, each of which induces a strongly <i>k</i>-connected tournament. This is clearly tight up to a constant factor, and it confirms a conjecture of Kühn, Osthus and Townsend (2016).</p>

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Partitioning a tournament into sub-tournaments of high connectivity

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月23日

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  • António Girão,
  • Shoham Letzter

摘要

We prove that there exists a constant \(c > 0\) c > 0 such that the vertices of every strongly \(c \cdot kt\) c · k t -connected tournament can be partitioned into t parts, each of which induces a strongly k-connected tournament. This is clearly tight up to a constant factor, and it confirms a conjecture of Kühn, Osthus and Townsend (2016).