A proper edge coloring of a simple graph G from some lists
assigned to the edges of G is of interest. A. Hilton and P.
Johnson (1990) considered a necessary condition for the list
coloring of a graph and called it Hall's condition. They
introduced the Hall index of a graph G, h′(G), as the smallest
positive integer m such that there exists a list coloring
whenever the lists are of length at least m and Hall's condition
is satisfied. They characterized all graphs G with h′(G)=1. In
this paper we characterize the graphs with Hall index 2.
Download TeX format
