A Note On 3-Choosability Of Planar Graphs

The article has tow main parts.PartⅠintroduces the choosability,another part introduces the game coloring chromatic number.A graph G is list L-colorable if for a given list assignment L={L(v):v∈V(G)},there exists a proper coloringφof G such thatφ(v)∈L(v)for each v∈V(G).If G is list L-colorable for every list assignment with |L(v)|≥k for all v∈V(G),then G is said to be k-choosable.We show in this note that every planar graph without any cycle of length in {4,6,7,8,9} is 3-choosable.In another part of this article,it introduces a new game coloring chromatic number and compares the differences between the two kinds of chromatic numbers.By labeling the vertices of graph, this article determines the chromatic number of several graphs.