摘要
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.
Abstract： Let G（V,E） be a simple graph, f be a k-proper total coloring of G, if f satisfing ｜｜Vi∪Ei｜-｜Vj∪Ej｜｜≤1（i≠j）, there Vi∪Ei={v｜f（v）=i}∪{e｜f（e）=i}, then f is called k-equitable total coloring of G （in brief, it is noted as eχT（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 Pn^k
are given, that is when n≥2k＋1, then eχT（Pkn）=5. So it is right for the conjecture in[5].
出处
《大学数学》
北大核心
2007年第3期59-64,共6页
College Mathematics
关键词
图
全染色
均匀全染色
graph
total coloring
equitable total coloring
