On list-coloring extendable outerplanar graphs
Joan P. Hutchinson · Ars Mathematica Contemporanea · 2012
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.