Shortest k-Cycle (Graph Cycles)

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

Related Problems

Generalizations: Shortest Cycle


$n$: 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, Corollary 4.2 link