The Cycle Counts of Graphs

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.

9 pp., 8 figures. v2: added data link. v3: 10 pp., improved writing; more computational details; added data for variant questions