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<p>For a nonnegative integer <i>k</i>, a graph <i>G</i> is said to be <i>k</i>-factor-critical if <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11227_2024_6902_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="TEX">\(G-Q\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <mo>-</mo> <mi>Q</mi> </mrow> </math></EquationSource> </InlineEquation> admits a perfect matching for any <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11227_2024_6902_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="78" /> </InlineMediaObject> <EquationSource Format="TEX">\(Q\subseteq V(G)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>Q</mi> <mo>⊆</mo> <mi>V</mi> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> with <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11227_2024_6902_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="59" /> </InlineMediaObject> <EquationSource Format="TEX">\(|Q|=k\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">|</mo> <mi>Q</mi> <mo stretchy="false">|</mo> <mo>=</mo> <mi>k</mi> </mrow> </math></EquationSource> </InlineEquation>. In this article, we prove spectral radius conditions for the existence of <i>k</i>-factor-critical graphs. Our result generalizes one previous result on perfect matchings of graphs. Furthermore, we claim that the bounds on spectral radius in Theorem 3.1 are sharp.</p>

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Spectral radius and k-factor-critical graphs

  • 期刊论文

  • 发表日期：

    2025年2月2日

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  • Sizhong Zhou,
  • Zhiren Sun,
  • Yuli Zhang

摘要

For a nonnegative integer k, a graph G is said to be k-factor-critical if \(G-Q\) G - Q admits a perfect matching for any \(Q\subseteq V(G)\) Q ⊆ V ( G ) with \(|Q|=k\) | Q | = k . In this article, we prove spectral radius conditions for the existence of k-factor-critical graphs. Our result generalizes one previous result on perfect matchings of graphs. Furthermore, we claim that the bounds on spectral radius in Theorem 3.1 are sharp.