Three-Coloring and List Three-Coloring of Graphs Without Induced Paths on Seven Vertices - Bonomo, Flavia; Chudnovsky, Maria; Maceli, Peter; Schaudt, Oliver; Stein, Maya; Zhong, Mingxian (Combinatorica (Budapest. 1981), 2018)
In this paper we present a polynomial time algorithm that determines if an input graph containing no induced seven-vertex path is 3-colorable. This affirmatively answers a question posed by Randerath, Schiermeyer and Tewes in 2002. Our algorithm also solves the list-coloring version of the 3-coloring problem, where every vertex is assigned a list of colors that is a subset of {1,2,3}, and gives an explicit coloring if one exists.