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<p>In this note, we prove a theorem covering an old well-known result of Chartrand, Kaugars, and Lick’s result in [Proc. Amer. Math. Soc. 32 (1972), 63–68]. As an application, we give a simpler proof of a theorem proved by Mader [J. Graph Theory 65 (2010), 61–69. (Theorem 1)], which we explicitly provide the construction process of the path <i>P</i> in <i>k</i>-connected graph <i>G</i> through a greedy algorithm, ensuring that <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(G-V(P)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <mo>-</mo> <mi>V</mi> <mo stretchy="false">(</mo> <mi>P</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> remains <i>k</i>-connected.</p>

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A note on a new result related to Chartrand, Kaugars and Lick’s theorem

  • 期刊论文

  • 发表日期：

    2025年12月17日

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  • Zhong Huang,
  • Meng Ji

摘要

In this note, we prove a theorem covering an old well-known result of Chartrand, Kaugars, and Lick’s result in [Proc. Amer. Math. Soc. 32 (1972), 63–68]. As an application, we give a simpler proof of a theorem proved by Mader [J. Graph Theory 65 (2010), 61–69. (Theorem 1)], which we explicitly provide the construction process of the path P in k-connected graph G through a greedy algorithm, ensuring that \(G-V(P)\) G - V ( P ) remains k-connected.