共查询到20条相似文献,搜索用时 21 毫秒
1.
We study the behavior of the 2-rank of the adjacency matrix of a graph under Seidel and Godsil–McKay switching, and apply the result to graphs coming from graphical Hadamard matrices of order . Starting with graphs from known Hadamard matrices of order 64, we find (by computer) many Godsil–McKay switching sets that increase the 2-rank. Thus we find strongly regular graphs with parameters , , and for almost all feasible 2-ranks. In addition we work out the behavior of the 2-rank for a graph product related to the Kronecker product for Hadamard matrices, which enables us to find many graphical Hadamard matrices of order for which the number of related strongly regular graphs with different 2-ranks is unbounded as a function of . The paper extends results from the article ‘Switched symplectic graphs and their 2-ranks’ by the first and the last author. 相似文献
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Building on recent work of Dvořák and Yepremyan, we show that every simple graph of minimum degree contains as an immersion and that every graph with chromatic number at least contains as an immersion. We also show that every graph on vertices with no independent set of size three contains as an immersion. 相似文献
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《Discrete Mathematics》2020,343(3):111721
The -additive codes are subgroups of , and can be seen as a generalization of linear codes over and . A -linear Hadamard code is a binary Hadamard code which is the Gray map image of a -additive code. A partial classification of these codes by using the dimension of the kernel is known. In this paper, we establish that some -linear Hadamard codes of length are equivalent, once is fixed. This allows us to improve the known upper bounds for the number of such nonequivalent codes. Moreover, up to , this new upper bound coincides with a known lower bound (based on the rank and dimension of the kernel). Finally, when we focus on , the full classification of the -linear Hadamard codes of length is established by giving the exact number of such codes. 相似文献
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We construct orthogonal arrays (of strength two) having a row that is repeated times, where is as large as possible. In particular, we consider OAs where the ratio is as large as possible; these OAs are termed optimal. We provide constructions of optimal OAs for any , albeit with large . We also study basic OAs; these are optimal OAs in which . We construct a basic OA with and , provided that a Hadamard matrix of order exists. This completely solves the problem of constructing basic OAs with , modulo the Hadamard matrix conjecture. 相似文献
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For a positive integer , a graph is -knitted if for each subset of vertices, and every partition of into (disjoint) parts for some , one can find disjoint connected subgraphs such that contains for each . In this article, we show that if the minimum degree of an -vertex graph is at least when , then is -knitted. The minimum degree is sharp. As a corollary, we obtain that -contraction-critical graphs are -connected. 相似文献
6.
《Discrete Mathematics》2022,345(8):112903
Graphs considered in this paper are finite, undirected and loopless, but we allow multiple edges. The point partition number is the least integer k for which G admits a coloring with k colors such that each color class induces a -degenerate subgraph of G. So is the chromatic number and is the point arboricity. The point partition number with was introduced by Lick and White. A graph G is called -critical if every proper subgraph H of G satisfies . In this paper we prove that if G is a -critical graph whose order satisfies , then G can be obtained from two non-empty disjoint subgraphs and by adding t edges between any pair of vertices with and . Based on this result we establish the minimum number of edges possible in a -critical graph G of order n and with , provided that and t is even. For the corresponding two results were obtained in 1963 by Tibor Gallai. 相似文献
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Le Chen Yaozhong Hu David Nualart 《Stochastic Processes and their Applications》2019,129(12):5073-5112
This paper studies the nonlinear stochastic partial differential equation of fractional orders both in space and time variables: where is the space–time white noise, , , and . Fundamental solutions and their properties, in particular the nonnegativity, are derived. The existence and uniqueness of solution together with the moment bounds of the solution are obtained under Dalang’s condition: . In some cases, the initial data can be measures. When , we prove the sample path regularity of the solution. 相似文献
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We consider subordinators in the domain of attraction at 0 of a stable subordinator (where ); thus, with the property that , the tail function of the canonical measure of , is regularly varying of index as . We also analyse the boundary case, , when is slowly varying at 0. When , we show that converges in distribution, as , to the random variable . This latter random variable, as a function of , converges in distribution as to the inverse of an exponential random variable. We prove these convergences, also generalised to functional versions (convergence in ), and to trimmed versions, whereby a fixed number of its largest jumps up to a specified time are subtracted from the process. The case produces convergence to an extremal process constructed from ordered jumps of a Cauchy subordinator. Our results generalise random walk and stable process results of Darling, Cressie, Kasahara, Kotani and Watanabe. 相似文献
11.
Let denote a Hermite process of order and self-similarity parameter . This process is -self-similar, has stationary increments and exhibits long-range dependence. When , it corresponds to the fractional Brownian motion, whereas it is not Gaussian as soon as . In this paper, we deal with a Vasicek-type model driven by , of the form . Here, and are considered as unknown drift parameters. We provide estimators for and based on continuous-time observations. For all possible values of and , we prove strong consistency and we analyze the asymptotic fluctuations. 相似文献
13.
Yongsheng Song 《Stochastic Processes and their Applications》2019,129(6):2066-2085
As is known, if is a -Brownian motion, a process of form , , is a non-increasing -martingale. In this paper, we shall show that a non-increasing -martingale cannot be form of or , , which implies that the decomposition for generalized -Itô processes is unique: For arbitrary , and non-increasing -martingales , if then we have , and. As an application, we give a characterization to the -Sobolev spaces introduced in Peng and Song (2015). 相似文献
14.
《Discrete Mathematics》2020,343(10):112010
Let be the -partite multigraph in which each part has size , where two vertices in the same part or different parts are joined by exactly edges or edges, respectively. It is proved that there exists a maximal set of edge-disjoint Hamilton cycles in for , the upper bound being best possible. The results proved make use of the method of amalgamations. 相似文献
15.
Émeline Schmisser 《Stochastic Processes and their Applications》2019,129(12):5364-5405
In this article, we consider a jump diffusion process , with drift function , diffusion coefficient and jump coefficient . This process is observed at discrete times . The sampling interval tends to 0 and the time interval tends to infinity. We assume that is ergodic, strictly stationary and exponentially -mixing. We use a penalized least-square approach to compute adaptive estimators of the functions and . We provide bounds for the risks of the two estimators. 相似文献
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Yinshan Chang Yiming Long Jian Wang 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2019,36(1):75-102
We consider a continuously differentiable curve in the space of real symplectic matrices, which is the solution of the following ODE: where and is a continuous path in the space of real matrices which are symmetric. Under a certain convexity assumption (which includes the particular case that is strictly positive definite for all ), we investigate the dynamics of the eigenvalues of when t varies, which are closely related to the stability of such Hamiltonian dynamical systems. We rigorously prove the qualitative behavior of the branching of eigenvalues and explicitly give the first order asymptotics of the eigenvalues. This generalizes classical Krein–Lyubarskii theorem on the analytic bifurcation of the Floquet multipliers under a linear perturbation of the Hamiltonian. As a corollary, we give a rigorous proof of the following statement of Ekeland: is a discrete set. 相似文献
19.
The paper investigates the properties of a class of resource allocation algorithms for communication networks: if a node of this network has requests to transmit and is idle, it tries to access the channel at a rate proportional to . A stochastic model of such an algorithm is investigated in the case of the star network, in which nodes can transmit simultaneously, but interfere with a central node 0 in such a way that node 0 cannot transmit while one of the other nodes does. One studies the impact of the log policy on these interacting communication nodes. A fluid scaling analysis of the network is derived with the scaling parameter being the norm of the initial state. It is shown that the asymptotic fluid behavior of the system is a consequence of the evolution of the state of the network on a specific time scale . The main result is that, on this time scale and under appropriate conditions, the state of a node with index is of the order of , with , where is a piecewise linear function. Convergence results on the fluid time scale and a stability property are derived as a consequence of this study. 相似文献
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In the two disjoint shortest paths problem ( 2-DSPP), the input is a graph (or a digraph) and its vertex pairs and , and the objective is to find two vertex-disjoint paths and such that is a shortest path from to for , if they exist. In this paper, we give a first polynomial-time algorithm for the undirected version of the 2-DSPP with an arbitrary non-negative edge length function. 相似文献