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arXiv · 2507.02260

The Cycle Counts of Graphs

Ryan McCulloch·Brendan D. McKay·Alireza Salahshoori·Thomas Zaslavsky
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Abstract

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.

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Ryan McCulloch, Brendan D. McKay, Alireza Salahshoori, Thomas Zaslavsky. 2025-11-28. The Cycle Counts of Graphs. https://arxiv.org/abs/2507.02260

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