Let a,b and k be nonnegative integers with a≥2 and b≥a(k+1)+2.A graph G is called a k-Hamiltonian graph if after deleting any k vertices of G the remaining graph of G has a Hamiltonian cycle.A graph G is said to hav...Let a,b and k be nonnegative integers with a≥2 and b≥a(k+1)+2.A graph G is called a k-Hamiltonian graph if after deleting any k vertices of G the remaining graph of G has a Hamiltonian cycle.A graph G is said to have a k-Hamiltonian[a,b]-factor if after deleting any k vertices of G the remaining graph of G admits a Hamiltonian[a,b]-factor.Let G is a k-Hamiltonian graph of order n with n≥a+k+2.In this paper,it is proved that G contains a k-Hamiltonian[a,b]-factor ifδ(G)≥a+k andδ(G)≥I(G)≥a-1+(a(k+1))/(b-2).展开更多
Let a,b,k be nonnegative integers with 2≤a<b.A graph G is called a k-Hamiltonian graph if G-U contains a Hamiltonian cycle for any subset U?V(G)with|U|=k.An[a,b]-factor F of G is called a Hamiltonian[a,b]-factor i...Let a,b,k be nonnegative integers with 2≤a<b.A graph G is called a k-Hamiltonian graph if G-U contains a Hamiltonian cycle for any subset U?V(G)with|U|=k.An[a,b]-factor F of G is called a Hamiltonian[a,b]-factor if F contains a Hamiltonian cycle.If G-U admits a Hamiltonian[a,b]-factor for any subset U?V(G)with|U|=k,then we say that G has a k-Hamiltonian[a,b]-factor.Suppose that G is a k-Hamiltonian graph of order n with n≥((a+b-4)(2 a+b+k-6))/(b-2)+k andδ(G)≥a+k.In this paper,it is proved that G admits a k-Hamiltonian[a,b]-factor if max{dG(x),dG(y)}≥((a-2)n+(b-2)k)/(a+b-4)+2 for each pair of nonadjacent vertices x and y in G.展开更多
如果，两个字母并成的一个单音 D 是 命令k 的为每顺序 S:v1 ， v2 ，， k 的 vk 不同顶点，在那里存在周期 C 以便 C 在指定 order.In 详细规格遇到 S 的顶点，我们说 D 是 命令k 的 hamiltonian 如果为每顺序 S:v1 ， v2 ，， k 的 vk...如果，两个字母并成的一个单音 D 是 命令k 的为每顺序 S:v1 ， v2 ，， k 的 vk 不同顶点，在那里存在周期 C 以便 C 在指定 order.In 详细规格遇到 S 的顶点，我们说 D 是 命令k 的 hamiltonian 如果为每顺序 S:v1 ， v2 ，， k 的 vk 不同顶点，在那里存在 hamiltonian 周期 C 以便 S 的顶点在指定 order.In 在 C 上被遇到这份报纸，为要订并且订 hamiltonian 的两个字母并成的一个单音的足够的条件被给了。展开更多
Projected Runge-Kutta （R-K） methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations （DAEs） in the Heisenberg form, are establi...Projected Runge-Kutta （R-K） methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations （DAEs） in the Heisenberg form, are established under the framework of Lagrangian multipliers. R-K methods combined with the technique of projections are then used to solve the DAEs. The basic idea of projections is to eliminate the constraint violations at the position, velocity, and acceleration levels, and to preserve the total energy of constrained Hamiltonian systems by correcting variables of the position, velocity, acceleration, and energy. Numerical results confirm the validity and show the high precision of the proposed method in preserving three levels of constraints and total energy compared with results reported in the literature.展开更多
In this paper, we present an algorithm for embedding an m-sequential k-ary tree into its optimal hypercube with dilation at most 2 and prove its correctness.
基金supported by the National Natural Science Foundation of China (Grant No. 11371009)the National Social Science Foundation of China (Grant No. 14AGL001)+1 种基金sponsored by Six Big Talent Peak of Jiangsu Province (Grant No. JY–022)333 Project of Jiangsu Province
文摘Let a,b and k be nonnegative integers with a≥2 and b≥a(k+1)+2.A graph G is called a k-Hamiltonian graph if after deleting any k vertices of G the remaining graph of G has a Hamiltonian cycle.A graph G is said to have a k-Hamiltonian[a,b]-factor if after deleting any k vertices of G the remaining graph of G admits a Hamiltonian[a,b]-factor.Let G is a k-Hamiltonian graph of order n with n≥a+k+2.In this paper,it is proved that G contains a k-Hamiltonian[a,b]-factor ifδ(G)≥a+k andδ(G)≥I(G)≥a-1+(a(k+1))/(b-2).
基金supported by the National Natural Science Foundation of China(Grant No.11371009)the National Social Science Foundation of China(Grant No.14AGL001)+1 种基金sponsored by Six Big Talent Peak of Jiangsu Province(Grant No.JY–022)333 Project of Jiangsu Province。
文摘Let a,b,k be nonnegative integers with 2≤a<b.A graph G is called a k-Hamiltonian graph if G-U contains a Hamiltonian cycle for any subset U?V(G)with|U|=k.An[a,b]-factor F of G is called a Hamiltonian[a,b]-factor if F contains a Hamiltonian cycle.If G-U admits a Hamiltonian[a,b]-factor for any subset U?V(G)with|U|=k,then we say that G has a k-Hamiltonian[a,b]-factor.Suppose that G is a k-Hamiltonian graph of order n with n≥((a+b-4)(2 a+b+k-6))/(b-2)+k andδ(G)≥a+k.In this paper,it is proved that G admits a k-Hamiltonian[a,b]-factor if max{dG(x),dG(y)}≥((a-2)n+(b-2)k)/(a+b-4)+2 for each pair of nonadjacent vertices x and y in G.
基金Foundation item： Supported by the National Natural Science Foundation of China（61070229） Supported by the Natural Science Foundation of Shanxi Province（2008011010）
文摘如果，两个字母并成的一个单音 D 是 命令k 的为每顺序 S:v1 ， v2 ，， k 的 vk 不同顶点，在那里存在周期 C 以便 C 在指定 order.In 详细规格遇到 S 的顶点，我们说 D 是 命令k 的 hamiltonian 如果为每顺序 S:v1 ， v2 ，， k 的 vk 不同顶点，在那里存在 hamiltonian 周期 C 以便 S 的顶点在指定 order.In 在 C 上被遇到这份报纸，为要订并且订 hamiltonian 的两个字母并成的一个单音的足够的条件被给了。
基金Project supported by the National Natural Science Foundation of China(No.11432010)the Doctoral Program Foundation of Education Ministry of China(No.20126102110023)+2 种基金the 111Project of China(No.B07050)the Fundamental Research Funds for the Central Universities(No.310201401JCQ01001)the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University(No.CX201517)
文摘Projected Runge-Kutta （R-K） methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations （DAEs） in the Heisenberg form, are established under the framework of Lagrangian multipliers. R-K methods combined with the technique of projections are then used to solve the DAEs. The basic idea of projections is to eliminate the constraint violations at the position, velocity, and acceleration levels, and to preserve the total energy of constrained Hamiltonian systems by correcting variables of the position, velocity, acceleration, and energy. Numerical results confirm the validity and show the high precision of the proposed method in preserving three levels of constraints and total energy compared with results reported in the literature.
文摘In this paper, we present an algorithm for embedding an m-sequential k-ary tree into its optimal hypercube with dilation at most 2 and prove its correctness.
