# Shortest k-Cycle (Graph Cycles)

(Redirected from Minimum Weight k-Cycle)

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## Description

Given a graph $G=(V,E)$ with non-negative weights, find a minimum weight cycle of length $k$.

## Related Problems

Generalizations: Shortest Cycle

## Parameters

$n$: number of vertices

$m$: number of edges

$k$: length of cycle

## Table of Algorithms

Currently no algorithms in our database for the given problem.

## Reductions FROM Problem

Problem | Implication | Year | Citation | Reduction |
---|---|---|---|---|

Min-Weight k-Clique | if: to-time: $O(nm^{\lceil k/{2} \rceil / \lambda - \epsilon})$ for any $\epsilon > {0}$ for $m = \Theta(n^{1+{1}/(\lambda - {1})}) edges and $n$ nodes where $\lambda = k - \lceil k/{2} \rceil + {1}$ then: from-time: $O(n^{k - \epsilon})$ for some $\epsilon > {0}$ |
2018 | https://arxiv.org/pdf/1712.08147v2.pdf, Corollary 4.2 | link |