---
tag: 5VZV0XJSAJ
kind: problem
name: 1-vs-2 cycles problem
sources:
  - wikipedia: en:78440969@r1365430189
    locator: 1-vs-2 cycles problem
    note: adopted
    mention: wikipedia://en/78440969
    sections: [Problem]
same_as:
  wikidata: Q131412142
  wikipedia: 1-vs-2 cycles problem
inventory: [5B8TH73619]
---

## Problem

In the theory of parallel algorithms, the **1-vs-2 cycles problem** concerns a simplified case of graph connectivity. The input to the problem is a [[2-regular graph|0KA4S8R39M]], forming either a single connected $n$-vertex cycle or two disconnected $n/2$-vertex cycles. The problem is to determine whether the input has one or two cycles.