Nondecreasing Triangle (Graph Triangle Problems)

Description

Given a tripartite graph with partitions $I, J, K$ and real edge weights, find a triangle $i \in I, j \in J, k \in K$ such that $w(i, k) \leq w(k, j) \leq w(i, j)$.

Related Problems

Generalizations: Triangle Detection

Related: Negative Triangle Detection, Negative Triangle Search, Negative Triangle Listing, Minimum Triangle, Triangle in Unweighted Graph, Triangle Collection*

Parameters

n: number of vertices

m: number of edges

Table of Algorithms

Currently no algorithms in our database for the given problem.

Reductions TO Problem

Problem	Implication	Year	Citation	Reduction
Triangle in Unweighted Graph	if: to-time: $T(n)$ for unweighted graph then: from-time: $O(n^{3/2} \sqrt{T(O(n))})$	2018	https://dl.acm.org/doi/pdf/10.1145/3186893, Theorem 7.1	link