关键词: 圈, 围长, 选色, 平面图, 欧拉公式

Abstract: The choice number of a graph G, denoted by χ_l(G), is the minimum number k such that if we give lists of k colors to each vertex of G, there is a vertex coloring of G where each vertex receives a color from its own list no matter what the lists are. Now, 3choosability of plane graphs has become a very active research branch, we have used the discharging method to research the subject, and at last we have shown that each plane graph of girth no less than 4 without 7-,8- and 15-cycles is of 3-choosability.

Key words: cycle, girth, choosability, plane graph, Euler’s formula