Author

Avinash Bhardwaj

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Preprint Sep 2026

The Geometry of Optimal Max-Cut SDP Solutions

When the semidefinite relaxation of Max-Cut is exact, its optimal cut sign vectors lie in the kernel of the optimal dual slack. We study when they span this kernel and which matrices can occur as certificates with this property. Our main result realizes every doubly nonnegative matrix with positive diagonal and rationa...

Avinash Bhardwaj, Chen Chen, Vishnu Narayanan · 0 citations

Preprint Sep 2026

The Complexity of Recognizing SDP Exactness for the Maximum Cut Problem

The standard semidefinite programming (SDP) relaxation of Max-Cut is exact when its optimum equals the maximum cut value. Delorme and Poljak resolved NP-completeness of recognizing exactness for weighted graphs and left the unweighted case open. We show that recognition is NP-complete even for connected simple unweight...

Avinash Bhardwaj · 0 citations

Preprint Aug 2026

Max-$k$-Cut via Node Features

It is shown that a greedy feature-balancing algorithm retains the classical $1-1/k$ worst-case approximation guarantee and recovers an optimal partition under feature dominance and for rank-$1$ feature graphs with nonnegative features, classical bounds of Chandra and Wong for greedy load balancing yield a computable op...

Avinash Bhardwaj, Hritiz Gogoi, Vishnu Narayanan · 1 citation