关于广义着色图的一个不等式
组合数学
2011-11-24 v1
摘要
设 G G G d 1 , d 2 , . . . , d n d_1,d_2,...,d_n d 1 , d 2 , ... , d n \V ( G ) \V(G) \V ( G ) n n n v ∈ \V ( G ) v\in\V(G) v ∈ \V ( G ) \D ( v ) \D(v) \D ( v ) \V ( G ) \V(G) \V ( G ) r r r \V ( G ) = V 1 ∪ V 2 ∪ . . . ∪ V r , V i ∩ V j = ∅ , , i ≠ j \V(G)=V_1\cup V_2\cup...\cup V_r,\quad V_i\cap V_j=\emptyset, \quad,i\neq j \V ( G ) = V 1 ∪ V 2 ∪ ... ∪ V r , V i ∩ V j = ∅ , , i = j \D ( v ) ≤ n − \abs V i \D(v)\leq n-\abs{V_i} \D ( v ) ≤ n − \abs V i ∀ v ∈ V i \forall v\in V_i ∀ v ∈ V i i = 1 , 2 , . . . , r i=1,2,...,r i = 1 , 2 , ... , r r r r \f ( G ) \f(G) \f ( G ) \f ( G ) ≥ n n − d ˉ ˉ , \f(G)\geq\frac n{n-\bar{\bar{d}}}, \f ( G ) ≥ n − d ˉ ˉ n , d ˉ ˉ = d 1 2 + d 2 2 + . . . + d n 2 n \bar{\bar{d}}=\sqrt{\dfrac{d_1^2+d_2^2+...+d_n^2}n} d ˉ ˉ = n d 1 2 + d 2 2 + ... + d n 2
引用
@article{arxiv.1111.5598,
title = {An Inequality for Generalized Chromatic Graphs},
author = {A. I. Bojilov and N. D. Nenov},
journal= {arXiv preprint arXiv:1111.5598},
year = {2011}
}
备注
5 pages