A Survey Of Max Degree Equitable Coloring Of Graphs

The coloring of planar graphs is an important topic in graph theory.It has a wide range of applications in many fields.And the equitable coloring is a particular case of planar graph colorings.Suppose(p is a proper k-coloring of graph G,and with color classes Vi.If for any i,j∈ {1,2,…*,k},||Vi|-|Vj|≤1 holds,that is to say,the sizes of any two color classes differ by at most one,then we say φ is the equitable k-coloring of G.As Hajnal and Szemeredi has already proved that G is equitably k-colorable when k≥ΔA(G)+ 1 in " Combinatorial Theory and Its Applications".Therefore,according to the studies on the equitable colorings of planar graphs,this thesis summarizes the literature and provides whether G is equitably k-colorable or not when k = Δ(G).This thesis introduces some research results in equitablyΔ-colorable not only with no restricted condition,but also with some limiting conditions.We provide some classical proofs as well.