K-%2c2n-的%5br，r%2b1，1%5d-染色.pdf

K2n [r,r + 1,1]- G = (V(G),E (G)) r, s, t, G [r,s,t]- V(G) ∪ E (G) {0,1,...,k − 1} c, v ,v , |c(v ) − c(v )| ≥ r; i j i j e ,e , |c(e ) − c(e )| ≥ s; v ∈ V(G), e ∈ E (G), i j i j i j |c(v ) − c(e )| ≥ t. G [r,s,t]- k G i j [r,s,t]- Æχ (G). K [r,r + 1,1]- r,s,t 2n χ (K ) = 6n − 4 n ≥ 3. r ≥ 3 Æ 2,3,1 2n (a) r ≥ 2n, χr,r+1,1(K2n) = r(2n − 1) + 1; (b) r 2n, (r + 1)(2n − 2) + 2 ≤ χr,r+1,1(K2n) ≤ (r + 1)(2n − 2) + 3; (c) r ≥ 3 r ≤ n − 1, χr,r+1,1(K2n) = (r + 1)(2n − 2) + 2. [r,s,t]- i K2n [r,r + 1,1]- [r,r + 1,1]-COLORING OF K2n 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 ) − c(v )| ≥ r for every two adjacent vertices v , i j i v , |c(e ) − c(e )| ≥ s for every two adjacent edges e , e , and |c(v ) − c(e )| ≥ t j i j i j i j for all pairs of incident vertices and edges, respectively. The[r,s,t]-chr