A Polynomial-Time Algorithm for Coloring Perfect Graphs Based on Walk Counting
A new polynomial-time algorithm is presented for optimally coloring perfect graphs using graph-theoretic operations and iterative walk counting.
A new polynomial-time algorithm for perfect graph coloring using graph-theoretic operations and walk counting.
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Applications
- →Graph theory, optimization, computer science.
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Abstract
More Like ThisWe 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.