Problem #84 defines:
The cycle set of a graph $G$ on $n$ vertices is a set $A \subseteq {3,\ldots,n}$ such that there is a cycle in $G$ of length $\ell$ if and only if $\ell \in A$. Let $f(n)$ count the number of possible such $A$.
The associated integer sequence is $f(3), f(4), f(5), \ldots$ — the number of distinct subsets of ${3,\ldots,n}$ that arise as the cycle set of some graph on $n$ vertices. This is the natural "possible OEIS" sequence for the problem.
A cursory OEIS search did not turn up an existing entry. Submitting this as a HELP WANTED issue because computing $f(n)$ for even modest $n$ requires enumerating graphs by cycle spectrum, which is nontrivial.
If anyone wants to take a crack at computing the first few terms, that would be enough to either (a) find a match in OEIS or (b) submit it as a new sequence (subject to the project's no-AI-submissions rule).
(Filed alongside PRs #283, #284, #285, #286, #287, #288, #289 in a Tier-1 OEIS-linking pass.)
Problem #84 defines:
The associated integer sequence is$f(3), f(4), f(5), \ldots$ — the number of distinct subsets of ${3,\ldots,n}$ that arise as the cycle set of some graph on $n$ vertices. This is the natural "possible OEIS" sequence for the problem.
A cursory OEIS search did not turn up an existing entry. Submitting this as a HELP WANTED issue because computing$f(n)$ for even modest $n$ requires enumerating graphs by cycle spectrum, which is nontrivial.
If anyone wants to take a crack at computing the first few terms, that would be enough to either (a) find a match in OEIS or (b) submit it as a new sequence (subject to the project's no-AI-submissions rule).
(Filed alongside PRs #283, #284, #285, #286, #287, #288, #289 in a Tier-1 OEIS-linking pass.)