P_n~k的均匀全染色

设G(V,E)是一个简单图,f是G的一个k-正常全染色,若f满足||Vi∪Ei|-|Vj∪Ej||≤1(i≠j),其中Vi∪Ei={v|f(v)=i}∪{e|f(e)=i},则称f为G的k-均匀全染色,简记为k-ETC.并称eχT(G)=min{k|G存在k-均匀全染色}为G的均匀全染色数.本文将通过很好的全染色方法得到eχT(Pkn)=5(n≥2k+1),并证明了对Pkn,5]中猜想是正确的.

The Equitable Total Coloring of Graph Pn^k

Let G(V,E) be a simple graph,f be a kproper total coloring of G,if f satisfing ||Vi∪Ei|-|Vj∪Ej||≤1 (i≠j),there Vi∪Ei={v|f(v)=i}∪{e|e∈E(G),f(e)=i},then f is called k-equitable total coloring of G(in brief,it is noted as k-ETC).χeT(G)=min{k|G has k-ETC} is called the equitable total chromatic number of G.In this paper good methods of 5-ETC coloring of Pkn are given,that is when n≥2k+1,then χeT(Pkn)=5.So it is right for the conjecture in 5].