<p>For graphs with fixed size <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3313_Article_IEq4.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="47" /> </InlineMediaObject> <EquationSource Format="TEX">\(m\ge 7\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>m</mi> <mo>≥</mo> <mn>7</mn> </mrow> </math></EquationSource> </InlineEquation>, we give a tight spectral condition that implies a graph contains a copy of <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3313_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="58" /> </InlineMediaObject> <EquationSource Format="TEX">\(K_1\vee P_4\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>K</mi> <mn>1</mn> </msub> <mo>∨</mo> <msub> <mi>P</mi> <mn>4</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>.</p>

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A note on a spectral condition for the existence of \(K_1\vee P_4\)

  • Jin Cai,
  • Leyou Xu

摘要

For graphs with fixed size \(m\ge 7\) m 7 , we give a tight spectral condition that implies a graph contains a copy of \(K_1\vee P_4\) K 1 P 4 .