The complexity of coloring graphs without long induced paths
Gerhard J. Woeginger, Ji rbreve, Jiřı́ Sgall · Acta Cybernetica · 2001
We discuss the computational complexity of determining the chromatic number of graphs without long induced paths. We prove NP-completeness of deciding whether a Ps-free graph is 5-colorable and of deciding whether a Pi2-free graph is 4-colorable. Moreover, we give a polynomial time algorithm for deciding whether a Ps-free graph is 3-colorable.