On list-coloring extendable outerplanar graphs

Abstract

We investigate a variation on Thomassen's 2- and 3-extendability of precoloring extensions for list-coloring graphs. For an outerplanar graph G with i, j ≤ 2, we say that G is {i, j}-extendable if for every pair of nonadjacent vertices x and y, whenever x is assigned an i-list, y is assigned a j-list, and all other vertices have a 3-list, G is list-colorable. We characterize the {1, 1}- and the {1, 2}-extendable outerplanar graphs and prove that every outerplanar graph is {2, 2}-extendable.