2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113577We give the first polynomial-time algorithm for coloring vertices of P_5-free graphs with k colors. This settles an open problem and generalizes several previously known results.Discrete MathematicsData Structures and AlgorithmsPolynomial-time algorithm for vertex k-colorability of P_5-free graphstext