Hoffman界是用邻接矩阵的特征值来表示正则图的独立数的上界。本文中,我们通过对独立数的概念进行推广,从而得到了一个Hoffman界的推广。作为一个应用,我们得到了EKR定理的饱和性,即当n≥2k+1时,对于集族ℱ∈([ n ]k),如果| ℱ |>(1+δ...Hoffman界是用邻接矩阵的特征值来表示正则图的独立数的上界。本文中,我们通过对独立数的概念进行推广,从而得到了一个Hoffman界的推广。作为一个应用,我们得到了EKR定理的饱和性,即当n≥2k+1时,对于集族ℱ∈([ n ]k),如果| ℱ |>(1+δ)(n−1k−1),那么ℱ中的2-匹配数至少为δ(1+δ)(n−1k−1)(n−k−1k−1)。同时,我们证明了当n≥2k+1时,对于集族A,ℬ∈([ n ]k),如果| A || ℬ |>(1+δ)(n−1k−1)2,那么A,ℬ中的2-匹配数至少为nδ2(n−k)(n−1k−1)(n−k−1k−1)。Hoffman’s bound is an upper on the independence number of a regular graph in terms of the eigenvalues of the adjacency matrix. In this paper, we get a generalization of Hoffman’s bound by extending of the definition of the independence number. As an application, we get the saturation of EKR theorem. In other words, we show that if ℱ∈([ n ]k)(n≥2k+1)with | ℱ |>(1+δ)(n−1k−1), then the number of 2-matching in ℱis greater than δ(1+δ)(n−1k−1)(n−k−1k−1). Meanwhile, we show that if A,ℬ∈([ n ]k)(n≥2k+1)with | A || ℬ |>(1+δ)(n−1k−1)2, then the number of 2-matching in A,ℬis greater than nδ2(n−k)(n−1k−1)(n−k−1k−1).展开更多
文摘Hoffman界是用邻接矩阵的特征值来表示正则图的独立数的上界。本文中,我们通过对独立数的概念进行推广,从而得到了一个Hoffman界的推广。作为一个应用,我们得到了EKR定理的饱和性,即当n≥2k+1时,对于集族ℱ∈([ n ]k),如果| ℱ |>(1+δ)(n−1k−1),那么ℱ中的2-匹配数至少为δ(1+δ)(n−1k−1)(n−k−1k−1)。同时,我们证明了当n≥2k+1时,对于集族A,ℬ∈([ n ]k),如果| A || ℬ |>(1+δ)(n−1k−1)2,那么A,ℬ中的2-匹配数至少为nδ2(n−k)(n−1k−1)(n−k−1k−1)。Hoffman’s bound is an upper on the independence number of a regular graph in terms of the eigenvalues of the adjacency matrix. In this paper, we get a generalization of Hoffman’s bound by extending of the definition of the independence number. As an application, we get the saturation of EKR theorem. In other words, we show that if ℱ∈([ n ]k)(n≥2k+1)with | ℱ |>(1+δ)(n−1k−1), then the number of 2-matching in ℱis greater than δ(1+δ)(n−1k−1)(n−k−1k−1). Meanwhile, we show that if A,ℬ∈([ n ]k)(n≥2k+1)with | A || ℬ |>(1+δ)(n−1k−1)2, then the number of 2-matching in A,ℬis greater than nδ2(n−k)(n−1k−1)(n−k−1k−1).
文摘为研究切丝宽度对卷烟主流烟气中7种Hoffmann成分释放量(CO,NNK,NH3,HCN,BaP,巴豆醛,苯酚)的影响,通过改变切丝宽度,测定卷烟主流烟气中7种Hoffmann成分的释放量.结果表明:在考察的切丝宽度范围内,随着切丝宽度的增加,烟气中CO,HCN和苯酚逐渐下降,NH3逐步上升,NNK和BaP先上升后下降,而巴豆醛和卷烟危害性指数保持不变;降低切丝宽度有利于选择性降低烟气中的NH3、BaP和巴豆醛,提高切丝宽度有利于选择性降低烟气中CO,HCN和苯酚.兼顾卷烟品质和卷烟减害,最佳切丝宽度为0.95 mm.
