List Coloring the Square of 2-connected Outerplanar Graph
Shen Bang-yu · Journal of Huaiyin Teachers College · 2009
The square of a graph G,denoted by G2,is a graph with the same vertex set such that two vertices are adjacent in G2 iff their distance is at most 2 in G.The list chromatic number of a graph G,denoted by χl(G) is the minimum number k such that if we give a list of k colors to each vertex of G,there is a vertex proper coloring of G where each vertex receives a color from its own list. Let G be a 2-connecded outerplanar graph with maximum degree Δ(G),then χl(G2)≤Δ(G)+2.