On CCE graphs of doubly partial orders

Let D be a digraph. The competition-common enemy graph (CCE graph) of D has the same set of vertices as D and an edge between vertices u and v if and only if there are vertices w and x in D such that (w,u), (w,v), (u,x), and (v,x) are arcs of D. We call a graph a CCE graph if it is the CCE graph of some digraph. In this paper, we show that if the CCE graph of a doubly partial order does not contain C₄ as an induced subgraph, it is an interval graph. We also show that any interval graph together with enough isolated vertices is the CCE graph of some doubly partial order.     

LA RECONSTRUCTION DES TOURNOIS SANS DIAMANT

We prove that if T is a tournament of order n > 6 in which any 4-sub-tournament is hamiltonian or transitive, then T is reconstructible in the sense of Ulam.     

Linear Ramsey numbers of sparse graphs

The Ramsey number R(G₁,G₂) of two graphs G₁ and G₂ is the least integer p so that either a graph G of order p contains a copy of G₁ or its complement G^c contains a copy of G₂. In 1973, Burr and Erd?s offered a total of $25 for settling the conjecture that there is a constant c = c(d) so that R(G,G)≤ c|V(G)| for all d‐degenerate graphs G, i.e., the Ramsey numbers grow linearly for d‐degenerate graphs. We show in this paper that the Ramsey numbers grow linearly for degenerate graphs versus some sparser graphs, arrangeable graphs, and crowns for example. This implies that the Ramsey numbers grow linearly for degenerate graphs versus graphs with bounded maximum degree, planar graphs, or graphs without containing any topological minor of a fixed clique, etc. © 2005 Wiley Periodicals, Inc. J Graph Theory     

Use of new composite materials for the determination of Cu, Cd, Mo, As, and Sb in biological samples by radiochemical neutron activation analysis

Summary  Vezetéknév     

Applications of interval arithmetic in solving polynomial equations by Wu''''s elimination method

Wu's elimination method is an important method for solving multivariate poly- nomial equations.In this paper,we apply interval arithmetic to Wu's method and convert the problem of solving polynomial equations into that of solving interval polynomial equa- tions.Parallel results such as zero-decomposition theorem are obtained for interval poly- nomial equations.The advantages of the new approach are two-folds:First,the problem of the numerical instability arisen from floating-point arithmetic is largely overcome.Second, the low efficiency of the algorithm caused by large intermediate coefficients introduced by exact compaction is dramatically improved.Some examples are provided to illustrate the effectiveness of the proposed algorithm.     

完全二部图Ka,b的迭线图L^m（Ka，b）的谱特征

本证明了当(a，b)不属于{(1，8)，(2，4)，(3，6)，(4，4)，(2s^2-s，2s^2 s))时，L^m(Ka,b)以谱为特征，其中a≤b，s≥2．     

(a,b,n)-临界图的几个充分条件

设G是一个图 .设g和f是两个定义在V(G)上的整值函数使得对V(G)所有顶点x有g(x) ≤f(x) .图G被称为 (g ,f,n) 临界图 ,如果删去G的任意n个顶点后的子图都含有G的 (g ,f) 因子 .本文给出了图是 (a ,b ,n) 临界图几个充分条件 ,即度和邻域条件 .进一步指出这些条件是最佳的 .     

高剥离类镁等电子序列的磁偶极M1和电四极E2光谱跃迁理论研究

利用全相对论性多组态Dirac-Fock广义平均能级方法，系统地计算了类镁离子3s3p磁偶极Ml^3P2--^3P1和电四极E2 ^2P2--^3P0(Z=20-103)光谱跃迁的能级间隔、跃迁几率和振子强度。计算中考虑了原子核的有限体积效应，进行了高阶Breit修正和QED修正，所得到的能级间隔和最近的实验数据及理论计算值进行了比较。计算结果表明：高原子序数的高荷电离子的磁偶极矩M1和电四极矩E2跃迁几率和中性原子的电偶极E1的相当，在ICF和MCF高温激光等离子体中，磁偶极矩M1和电四极矩E2跃迁过程不容被忽视。     

Large families of mutually embeddable vertex‐transitive graphs

For each infinite cardinal κ, we give examples of 2^κ many non‐isomorphic vertex‐transitive graphs of order κ that are pairwise isomorphic to induced subgraphs of each other. We consider examples of graphs with these properties that are also universal, in the sense that they embed all graphs with smaller orders as induced subgraphs. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 99–106, 2003     

图的边韧性度

文[1]中,定义图G(V,E)的边韧性度定义为min{(|S|+T(G-S))/(ω(G-S)):S?E(G)},这里,T-(G-S)和ω(G-S)分别表示G-S中最大分支的顶点数和连通分支数.这是一个能衡量网络图稳定性较好的参数,因为它不仅考虑到了图G-S的分支数也考虑到了它的阶数.在以前的工作中,作者得到了边韧性度图的一个充要条件.利用这些结果证明了K-树是严格边韧性度图,并找到了边韧性度与较高阶的边坚韧度和边坚韧度之间的关系.