[r, s, t]-Colorings of graphs
[r, s, t]-Colorings of graphs
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DOI：
10.1016/j.disc.2006.06.030
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
A. Kemnitz;M. Marangio
中科院分区：
文献类型：
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作者：
A. Kemnitz;M. Marangio
Given non-negative integers r, s, and t, an [r,s,t]-coloring of a graph G=(V(G),E(G)) is a mapping c from V(G)∪E(G) to the color set {0,1,…,k-1} such that |c(vi)-c(vj)|⩾r for every two adjacent vertices vi,vj, |c(ei)-c(ej)|⩾s for every two adjacent edges ei,ej, and |c(vi)-c(ej)|⩾t for all pairs of incident vertices and edges, respectively. The [r,s,t]-chromatic numberχr,s,t(G) of G is defined to be the minimum k such that G admits an [r,s,t]-coloring. This is an obvious generalization of all classical graph colorings since c is a vertex coloring if r=1, s=t=0, an edge coloring if s=1, r=t=0, and a total coloring if r=s=t=1, respectively. We present first results on χr,s,t(G) such as general bounds and also exact values, for example if min{r,s,t}=0 or if G is a complete graph.
