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<p>Whitney proved that if two 3-connected graphs <i>G</i> and <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="493_2025_160_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(G'\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>G</mi> <mo>′</mo> </msup> </math></EquationSource> </InlineEquation> have the same set of cycles (or equivalently, the same set of cuts) then <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="493_2025_160_Article_IEq2.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="55" /> </InlineMediaObject> <EquationSource Format="TEX">\(G=G'\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <mo>=</mo> <msup> <mi>G</mi> <mo>′</mo> </msup> </mrow> </math></EquationSource> </InlineEquation>. We characterize when two 4-connected signed graphs have the same set of even cycles, and we characterize when two 4-connected grafts have the same set of even cuts.</p>

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Signed graphs with the same even cycles

  • 期刊论文

  • 发表日期：

    2025年7月4日

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  • Bertrand Guenin,
  • Cheolwon Heo,
  • Irene Pivotto

摘要

Whitney proved that if two 3-connected graphs G and \(G'\) G ′ have the same set of cycles (or equivalently, the same set of cuts) then \(G=G'\) G = G ′ . We characterize when two 4-connected signed graphs have the same set of even cycles, and we characterize when two 4-connected grafts have the same set of even cuts.