[r,s,t]-Coloring of K
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Authors: | Changqing Xu Xianli Ma Shouliang Hua |
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Institution: | 1. Department of Applied Mathematics, Hebei University of Technology, Tianjin, 300401, People’s Republic of China 2. Department of Mathematics, Anyang University of Technology, Anyang, Henan, 455100, People’s Republic of China
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Abstract: | Let G=(V(G),E(G)) be a simple graph. Given non-negative integers r,s, and t, an r,s,t]-coloring of G is a mapping c from V(G)∪E(G) to the color set {0,1,…,k?1} such that |c(v i )?c(v j )|≥r for every two adjacent vertices v i ,v j , |c(e i )?c(e j )|≥s for every two adjacent edges e i ,e j , and |c(v i )?c(e j )|≥t for all pairs of incident vertices and edges, respectively. The r,s,t]-chromatic number χ r,s,t (G) of G is defined to be the minimum k such that G admits an r,s,t]-coloring. We determine χ r,s,t (K n,n ) in all cases. |
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