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<p>A vertex subset <i>H</i> of a 3-connected finite graph <i>G</i> is said to be <i>contractible</i> if <i>G</i>(<i>H</i>) is connected and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(G - H\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <mo>-</mo> <mi>H</mi> </mrow> </math></EquationSource> </InlineEquation> is biconnected. It is proved that every 3-connected graph with at least&#xa0;13 vertices has a contractible set with&#xa0;5 vertices. Moreover, there is a 3-connected graph with&#xa0;12 vertices, that has no contractible set with&#xa0;5 vertices. Bibliography: 12 titles.</p>

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EVERY 3-CONNECTED GRAPH WITH AT LEAST 13 VERTICES HAS A CONTRACTIBLE SET WITH 5 VERTICES

  • 期刊论文

  • 发表日期：

    2026年3月19日

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  • N. Yu. Vlasova

摘要

A vertex subset H of a 3-connected finite graph G is said to be contractible if G(H) is connected and \(G - H\) G - H is biconnected. It is proved that every 3-connected graph with at least 13 vertices has a contractible set with 5 vertices. Moreover, there is a 3-connected graph with 12 vertices, that has no contractible set with 5 vertices. Bibliography: 12 titles.