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<p>We prove that an inseparable graph can have any positive number of cycles with the six exceptions 2, 4, 5, 8, 9, 16, and that an inseparable cubic graph has the additional exceptions 1 and 13. The exceptions for simple inseparable cubic graphs are unknown.</p>

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The Cycle Counts of Graphs

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年6月1日

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  • Ryan McCulloch,
  • Brendan D. McKay,
  • Alireza Salahshoori,
  • Thomas Zaslavsky

摘要

We prove that an inseparable graph can have any positive number of cycles with the six exceptions 2, 4, 5, 8, 9, 16, and that an inseparable cubic graph has the additional exceptions 1 and 13. The exceptions for simple inseparable cubic graphs are unknown.