Abstract
Let s and t be positive integers. We use Pt to denote the path with t vertices and K1,s to
denote the complete bipartite graph with parts of size 1 and s respectively. The one-subdivision
of K1,s is obtained by replacing every edge {u, v} of K1,s by two edges {u, v} and {u, v} with a
new vertex w. In this paper, we give a polynomial-time algorithm for the list 3-coloring problem
restricted to the class of Pt-free graph with no induced 1-subdivision of K1,s.