# Min-Weight k-Clique (Clique Problems)

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## Description

Given a graph $G = (V, E)$, find the $k$-clique of minimum weight.

## Related Problems

Generalizations: k-Clique

Related: Enumerating Maximal Cliques, arbitrary graph, Exact k-Clique, Max-Weight k-Clique

## Parameters

$n$: number of vertices

$m$: number of edges

$k$: size of clique

## Table of Algorithms

Currently no algorithms in our database for the given problem.

## Reductions TO Problem

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

Minimum Weight k-Cycle | 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 |