Tag · 2 problems · 2 fields

Open problems tagged cycles

2 problems in the Math Lab index touch cycles, spanning Number Theory, Graph Theory. Each carries a precise statement, an honest status, and a computational line of attack.

Collatz conjectureNumber Theorylive lab

Halve n if even, map n to 3n + 1 if odd, repeat. The conjecture: every positive integer eventually reaches 1.

a.k.a. 3n + 1 problem · Syracuse problem · hailstone problem · Ulam's conjecture

Caccetta–Häggkvist conjectureGraph Theoryuntouched

Every digraph on n vertices with minimum out-degree r contains a directed cycle of length at most ⌈n/r⌉.