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arXiv · 2607.09309

A Polynomial-Time Algorithm for Coloring Perfect Graphs Based on Walk Counting

Amir Ali Ahmadi·Pravesh K. Kothari·Yukai Tang
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Abstract

We present a polynomial-time algorithm for optimally coloring perfect graphs that is based entirely on graph-theoretic operations. At its core, the algorithm decides whether a perfect graph contains a clique of a given size by iteratively counting walks in the graph with certain weights assigned to its edges and nonedges. These weights are initialized according to a uniform scheme and then updated in each iteration based on the walk counts from the previous iteration.

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Amir Ali Ahmadi, Pravesh K. Kothari, Yukai Tang. 2026-07-10. A Polynomial-Time Algorithm for Coloring Perfect Graphs Based on Walk Counting. https://arxiv.org/abs/2607.09309

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