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<p>Modular-width and neighborhood diversity are structural graph parameters used in parameterized complexity. For some problems, like the Harmless Set Problem, FPT algorithms are known when the parameter is the neighborhood diversity, while remaining open for modular-width. We study the Iterated-Type Partition (ITP), an intermediate structural measure between these two, and show that ITP is equivalent to the recently introduced cograph-modular cardinality.</p>

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Some Results on the Relationship of Modular Parameters on Graphs

  • 期刊论文

  • 发表日期：

    2025年10月27日

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  • Leandro Freitas de Souza,
  • Vinicius F. dos Santos

摘要

Modular-width and neighborhood diversity are structural graph parameters used in parameterized complexity. For some problems, like the Harmless Set Problem, FPT algorithms are known when the parameter is the neighborhood diversity, while remaining open for modular-width. We study the Iterated-Type Partition (ITP), an intermediate structural measure between these two, and show that ITP is equivalent to the recently introduced cograph-modular cardinality.