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1.
Solution to an extremal problem on bigraphic pairs with a <Emphasis Type="Italic">Z</Emphasis><Subscript>3</Subscript>-connected realization
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Let S=(a1,...,am; b1,...,bn), where a1,...,am and b1,...,bn are two nonincreasing sequences of nonnegative integers. The pair S=(a1,...,am; b1,...,bn) is said to be a bigraphic pair if there is a simple bipartite graph G=(X ∪ Y, E) such that a1,...,am and b1,...,bn are the degrees of the vertices in X and Y, respectively. Let Z3 be the cyclic group of order 3. Define σ(Z3, m, n) to be the minimum integer k such that every bigraphic pair S=(a1,...,am; b1,...,bn) with am, bn ≥ 2 and σ(S)=a1 +... + am ≥ k has a Z3-connected realization. For n=m, Yin[Discrete Math., 339, 2018-2026 (2016)] recently determined the values of σ(Z3, m, m) for m ≥ 4. In this paper, we completely determine the values of σ(Z3, m, n) for m ≥ n ≥ 4. 相似文献
2.
Let G be a graph of order n, and let a and b be integers such that 1a<b. Let δ(G) be the minimum degree of G. Then we prove that if δ(G)(k−1)a, n(a+b)(k(a+b)−2)/b, and |NG(x1)NG(x2)NG(xk)|an/(a+b) for any independent subset {x1,x2,…,xk} of V(G), where k2, then G has an [a,b]-factor. This result is best possible in some sense. 相似文献
3.
We give a bijective proof for the identity an+2=8bn, where an is the number of noncrossing simple graphs with n (possibly isolated) vertices and bn is the number of noncrossing graphs without isolated vertices and with n (possibly multiple) edges. 相似文献
4.
《Discrete Mathematics》1999,200(1-3):137-147
We form squares from the product of integers in a short interval [n, n + tn], where we include n in the product. If p is prime, p|n, and (2p) > n, we prove that p is the minimum tn. If no such prime exists, we prove tn √5n when n> 32. If n = p(2p − 1) and both p and 2p − 1 are primes, then tn = 3p> 3 √n/2. For n(n + u) a square > n2, we conjecture that a and b exist where n < a < b < n + u and nab is a square (except n = 8 and N = 392). Let g2(n) be minimal such that a square can be formed as the product of distinct integers from [n, g2(n)] so that no pair of consecutive integers is omitted. We prove that g2(n) 3n − 3, and list or conjecture the values of g2(n) for all n. We describe the generalization to kth powers and conjecture the values for large n. 相似文献
5.
Stability of Periodic Orbits and Return Trajectories of Continuous Multi-valued Maps on Intervals
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Let I be a compact interval of real axis R, and(I, H) be the metric space of all nonempty closed subintervals of I with the Hausdorff metric H and f : I → I be a continuous multi-valued map. Assume that Pn =(x_0, x_1,..., xn) is a return tra jectory of f and that p ∈ [min Pn, max Pn] with p ∈ f(p). In this paper, we show that if there exist k(≥ 1) centripetal point pairs of f(relative to p)in {(x_i; x_i+1) : 0 ≤ i ≤ n-1} and n = sk + r(0 ≤ r ≤ k-1), then f has an R-periodic orbit, where R = s + 1 if s is even, and R = s if s is odd and r = 0, and R = s + 2 if s is odd and r 0. Besides,we also study stability of periodic orbits of continuous multi-valued maps from I to I. 相似文献
6.
D. D. Anderson
David F. Anderson
《Journal of Pure and Applied Algebra》1992,80(3):217-235For an atomic integral domain R, define(R)=sup{mn|x1xm=y1yn, each xi,yjεR is irreducible}. We investigate (R), with emphasis for Krull domains R. When R is a Krull domain, we determine lower and upper bounds for (R); in particular,(R)≤max{|Cl(R)| 2, 1}. Moreover, we show that for any real numbers r≥1 or R=∞, there is a Dedekind domain R with torsion class group such that (R)=r. 相似文献
7.
Hansjoachim Walther 《Discrete Applied Mathematics》2002,120(1-3):263-274
A face F of a polyhedral graph G(V,E,F) is an a1,a2,…,al-face if is an l-gon and the degrees d(xi) of the vertices xiV incident with in the cyclic order are ai,i=1,2,…,l. The lexicographic minimum b1,b2,…,bl such that is a b1,b2,…,bl-face is the type of . All polyhedral graphs having only one type of faces are listed. It is proved that the set of triangulations having only faces of different types is non-empty and finite. 相似文献
8.
In this paper we investigate the behaviour of the solutions of equations ΣI=1n aixi = b, where Σi=1n, ai = 0 and b ≠ 0, with respect to colorings of the set N of positive integers. It turns out that for any b ≠ 0 there exists an 8-coloring of N, admitting no monochromatic solution of x3 − x2 = x2 − x1 + b. For this equation, for b odd and 2-colorings, only an odd-even coloring prevents a monochromatic solution. For b even and 2-colorings, always monochromatic solutions can be found, and bounds for the corresponding Rado numbers are given. If one imposes the ordering x1 < x2 < x3, then there exists already a 4-coloring of N, which prevents a monochromatic solution of x3 − x2 = x2 − x1 + b, where b ε N. 相似文献
9.
10.
We construct the polynomial pm,n* of degree m which interpolates a given real-valued function f L2[a, b] at pre-assigned n distinct nodes and is the best approximant to f in the L2-sense over all polynomials of degree m with the same interpolatory character. It is shown that the L2-error pm,n* − f → 0 as m → ∞ if f C[a, b]. 相似文献
11.
S. Zhou 《Applied Mathematics Letters》1998,11(6):15-18
Let M be a weighted binary matroid and w1 < … < wm be the increasing sequence of all possible distinct weights of bases of M. We give a sufficient condition for the property that w1, …, wm is an arithmetical progression of common difference d. We also give conditions which guarantee that wi+1 − wi ≤ d, 1 ≤ i ≤ m −1. Dual forms for these results are given also. 相似文献
12.
Maximal IM-unextendable graphs 总被引:3,自引:0,他引:3
A graph G is maximal IM-unextendable if G is not induced matching extendable and, for every two nonadjacent vertices x and y, G+xy is induced matching extendable. We show in this paper that a graph G is maximal IM-unextendable if and only if G is isomorphic to Mr(Ks(Kn1Kn2Knt)), where Mr is an induced matching of size r, r1, t=s+2, and each ni is odd. 相似文献
13.
Every closed nanorientable 3-manifold M can be obtained as the union of three orientable handlebodies V1, V2, V3 whose interiors are pairwise disjoint. If gi denotes the genus of Vi, g1g2g3, we say that M has tri-genus (g1, g2, g3), if in terms of lexicographical ordering, the triple (g1, g2, g3) is minimal among all such decompositions of M into orientable handlebodies. We relate the tri-genus of M to the genus of a surface that represents the dual of the first Stiefel-Whitney class of M. This is used to determine g1 and g2. 相似文献
14.
Xuding Zhu 《Discrete Mathematics》1998,190(1-3):215-222
Suppose G is a graph. The chromatic Ramsey number rc(G) of G is the least integer m such that there exists a graph F of chromatic number m for which the following is true: for any 2-colouring of the edges of F there is a monochromatic subgraph isomorphic to G. Let Mn = min[rc(G): χ(G) = n]. It was conjectured by Burr et al. (1976) that Mn = (n − 1)2 + 1. This conjecture has been confirmed previously for n 4. In this paper, we shall prove that the conjecture is true for n = 5. We shall also improve the upper bounds for M6 and M7. 相似文献
15.
Georg Heinig 《Linear algebra and its applications》2002,340(1-3):1-13
The structure of the kernel of block Toeplitz-plus-Hankel matrices R=[aj−k+bj+k], where aj and bj are the given p×q blocks with entries from a given field, is investigated. It is shown that R corresponds to two systems of at most p+q vector polynomials from which a basis of the kernel of R and all other Toeplitz-plus-Hankel matrices with the same parameters aj and bj can be built. The main result is an analogue of a known kernel structure theorem for block Toeplitz and block Hankel matrices. 相似文献
16.
If the edges of a graph G are colored using k colors, we consider the color distribution for this coloring a=(a1,a2,…,ak), in which ai denotes the number of edges of color i for i=1,2,…,k. We find inequalities and majorization conditions on color distributions of the complete bipartite graph Kn,n which guarantee the existence of multicolored subgraphs: in particular, multicolored forests and trees. We end with a conjecture on partitions of Kn,n into multicolored trees. 相似文献
17.
On a problem about face polynomials 总被引:1,自引:0,他引:1
Wei Li 《Journal of Pure and Applied Algebra》1989,60(3):269-272
It is proved that an R-automorphism of polynomial ring R[x1,…,xn] is completely determined by its face polynomials, where R is a reduced commutative ring and n≥2. An example is given which shows that the condition R being reduced cannot be weakened. 相似文献
18.
Imre Brny 《Discrete Mathematics》1982,40(2-3):141-152
The following theorem is proved. If the sets
and a εn+1i=1 conv Vi, then there exist elements vi ε Vi (i=1…,n+1) such that a ε conv{v1,…,vn+1}. This is generalization of Carathéodory's theorem. By applying this and similar results some open questions are answered. 相似文献
19.
Let H be a Hopf algebra over a field k and let H A → A, h a → h.a, be an action of H on a commutative local Noetherian kalgebra (A, m). We say that this action is linearizable if there exists a minimal system x1, …, xn of generators of the maximal ideal m such that h.xi ε kx1 + …+ kxn for all h ε H and i = 1, …, n. In the paper we prove that the actions from a certain class are linearizable (see Theorem 4), and we indicate some consequences of this fact. 相似文献
20.
R. A. Kasonga 《Stochastic Processes and their Applications》1988,30(2):263-275
Consider the following Itô stochastic differential equation dX(t) = ƒ(θ0, X(t)) dt + dW(t), where (W(t), t 0), is a standard Wiener process in RN. On the basis of discrete data 0 = t0 < t1 < …<tn = T; X(t1),...,X(tn) we would like to estimate the parameter θ0. We shall define the least squares estimator
and show that under some regularity conditions,
is strongly consistent. 相似文献