图的全彩虹连通数的良好上界
组合数学
2015-01-09 v1
摘要
全染色图是指图 G G G G G G G G G G G G G G G G G G t r c ( G ) trc(G) t r c ( G ) G G G G G G 2 d i a m ( G ) − 1 ≤ t r c ( G ) ≤ 2 n − 3 2diam(G)-1\leq trc(G)\leq 2n-3 2 d iam ( G ) − 1 ≤ t r c ( G ) ≤ 2 n − 3 d i a m ( G ) diam(G) d iam ( G ) G G G n n n G G G n n n δ \delta δ G G G δ ≥ n − 2 − 1 \delta\geq\sqrt{n-2}-1 δ ≥ n − 2 − 1 n ≥ 291 n\geq 291 n ≥ 291 t r c ( G ) ≤ 6 n / ( δ + 1 ) + 28 trc(G)\leq6n/{(\delta+1)}+28 t r c ( G ) ≤ 6 n / ( δ + 1 ) + 28 16 ≤ δ ≤ n − 2 − 2 16\leq\delta\leq\sqrt{n-2}-2 16 ≤ δ ≤ n − 2 − 2 t r c ( G ) ≤ 7 n / ( δ + 1 ) + 32 trc(G)\leq7n/{(\delta+1)}+32 t r c ( G ) ≤ 7 n / ( δ + 1 ) + 32 6 ≤ δ ≤ 15 6\leq\delta\leq15 6 ≤ δ ≤ 15 t r c ( G ) ≤ 7 n / ( δ + 1 ) + 4 C ( δ ) + 12 trc(G)\leq7n/{(\delta+1)}+4C(\delta)+12 t r c ( G ) ≤ 7 n / ( δ + 1 ) + 4 C ( δ ) + 12 C ( δ ) = e 3 log ( δ 3 + 2 δ 2 + 3 ) − 3 ( log 3 − 1 ) δ − 3 − 2 C(\delta)=e^{\frac{3\log({\delta}^3+2{\delta}^2+3)-3(\log3-1)}{\delta-3}}-2 C ( δ ) = e δ − 3 3 l o g ( δ 3 + 2 δ 2 + 3 ) − 3 ( l o g 3 − 1 ) − 2 δ \delta δ n n n t r c ( G ) trc(G) t r c ( G ) δ = 3 \delta=3 δ = 3 t r c ( G ) ≤ 7 n / 4 − 3 trc(G)\leq 7n/4-3 t r c ( G ) ≤ 7 n /4 − 3 δ = 4 \delta=4 δ = 4 t r c ( G ) ≤ 8 n / 5 − 13 / 5 trc(G)\leq8n/5-13/5 t r c ( G ) ≤ 8 n /5 − 13/5 δ = 5 \delta=5 δ = 5 t r c ( G ) ≤ 3 n / 2 − 3 trc(G)\leq3n/2-3 t r c ( G ) ≤ 3 n /2 − 3 δ ≥ n − 2 − 1 \delta\geq\sqrt{n-2}-1 δ ≥ n − 2 − 1
引用
@article{arxiv.1501.01806,
title = {Good upper bounds for the total rainbow connection of graphs},
author = {Hui Jiang and Xueliang Li and Yingying Zhang},
journal= {arXiv preprint arXiv:1501.01806},
year = {2015}
}
备注
8 pages