The Cycle Counts of Graphs

Graphs and Combinatorics 2026 Open access

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Authors: Ryan McCulloch, Brendan D. McKay, Alireza Salahshoori, Thomas Zasĺavsky
DOI: 10.1007/s00373-026-03047-3
Cited by: 0

Abstract

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.

Fields of Study & Subjects

Advanced Graph Theory Research

Publication details

Journal / source
Graphs and Combinatorics
Volume
42
Issue
3
Publication date
1 June 2026
Language
EN