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<p>We prove Jones’ famous conjecture for Halin graphs and a somewhat more general class of graphs, too. A based planar graph is a planar one that has a face adjacent to every other face. We confirm Jones’ conjecture for based planar graphs. Namely, if a based planar graph does not contain <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(k+1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> vertex-disjoint cycles, then it suffices to delete 2<i>k</i> vertices to make it acyclic.</p>

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Jones’ Conjecture for Halin Graphs and a Bit More

  • 期刊论文

  • 发表日期：

    2025年12月12日

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  • Pál Bärnkopf,
  • Ervin Győri

摘要

We prove Jones’ famous conjecture for Halin graphs and a somewhat more general class of graphs, too. A based planar graph is a planar one that has a face adjacent to every other face. We confirm Jones’ conjecture for based planar graphs. Namely, if a based planar graph does not contain \(k+1\) k + 1 vertex-disjoint cycles, then it suffices to delete 2k vertices to make it acyclic.