List 3-coloring Pt-free graphs with no induced 1-subdivision of K1, s

Abstract Let s and t be positive integers. We use P t to denote the path with t vertices and K 1 , s to denote the complete bipartite graph with parts of size 1 and s respectively. The one-subdivision of K 1 , s is obtained by replacing every edge { u , v } of K 1 , s by two edges { u , w } and { v , w } 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 P t -free graph with no induced 1-subdivision of K 1 , s .