Tootfinder

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

The Cycle Counts of Graphs
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 sole additional exception 13.