Injective List Coloring Of Planar Graphs

All graphs considered in this paper are finite simple graphs.For a planar graph G,the distance between vertex set,edge set,maximum,minimum,face set,girth and two points u,v of G are denoted as V(G),E(G),?(G),?(G),F(G),g(G)and dG(u,v).An injective k—coloring of a graph G is an assignment of k colors to the vertices of G so that any two vertices with a common neighbor receive distinct colors.The injective chromatic number ?i(G),is the least k such that G is injectively k—colorable.A list configuration of graph G is to allocate a usable color set L(v)to each vertex v ?V(G).A list configuration of L for G is to allocate a list configuration of L,if a injective-coloring? satisfy ?(V)? L(v)((?)?V(G)),then ? is a injective L-coloring of G.The coloring theory of graphs is an important field in graph theory.With the development of technologies,the types of coloring of graphs are increasing.For example,list coloring,linear coloring,edge distinguishable coloring,star coloring and so on.As early as the beginning of this century,scholars Hahn proposed a new coloring injective-coloring.Injective-coloring is not necessarily abnormal coloring.Scholars Kim and Oum Scholars have given the following theorems:For any simple graph H,have ?i(H)??(H2)?2?i(H).This theorem reflects the injective-coloring problem of graphs very intuitively.It is related to the coloring problem of square graphs.This dissertation mainly studies some conclusions about the injective-list coloring of planar graphs.In Chapter 2,we study the plane graph G whose girth of at least 5 and ?(G)?11,have ?il(G)??(G)+4.In Chapter 3,we study the plane graph G which is 5--cycles and 5--cycles disjiont and ?(G)?18,have ?i1(G)??(G)+6.