On The Number Of Sets Of Cycle Lengths

A set S of integers is called a cycle set on {1, 2, . . .,n} if there exists a graph G on n vertices such that the set of lengths of cycles in G is S. Erdős conjectured that the number of cycle sets on {1, 2, . . .,n} is o(2n). In this paper, we verify this conjecture by proving that there exists an absolute constant c ≥ 0.1 such that the number of cycle sets on {1, 2, . . .,n} is \( o{\left( {2^{{n - n^{c} }} } \right)} \).

This is a preview of subscription content, access via your institution.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Jacques Verstraëte.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Verstraëte, J. On The Number Of Sets Of Cycle Lengths. Combinatorica 24, 719–730 (2004). https://doi.org/10.1007/s00493-004-0043-6

Download citation

Mathematics Subject Classification (2000):

  • 05C38