Min-Weight k-Clique (Clique Problems)

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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


$n$: 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