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Two graphs G and H are chromatically equivalent if they have the same chromatic polynomial. In some cases, chromatically equivalent graphs may differ by only one edge, that is, \(G\backslash e \cong H\backslash f\) for an edge \(e \in E(G)\) and edge \(f \in E(H)\) . We provide an example that shows that not all pairs of chromatically equivalent chordal graphs have this property.

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Chromatically Equivalent Chordal Graphs

  • 章节

  • 发表日期：

    2025年

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  • Fengming Dong,
  • Alex Fink,
  • Tony Li,
  • Brendan McKay,
  • Kerri Morgan,
  • Gordon Royle,
  • Lluís Vena,
  • Meiqiao Zhang

摘要

Two graphs G and H are chromatically equivalent if they have the same chromatic polynomial. In some cases, chromatically equivalent graphs may differ by only one edge, that is, \(G\backslash e \cong H\backslash f\) for an edge \(e \in E(G)\) and edge \(f \in E(H)\) . We provide an example that shows that not all pairs of chromatically equivalent chordal graphs have this property.