Shortest k-Cycle (Graph Cycles)

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