共查询到20条相似文献,搜索用时 31 毫秒
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Yinghui Wang 《Discrete Mathematics》2019,342(5):1325-1335
We define and study a variant of the Stanley depth which we call total depth for partially ordered sets (posets). This total depth is the most natural variant of Stanley depth from – the poset of nonempty subsets of ordered by inclusion – to any finite poset. In particular, the total depth can be defined for the poset of nonempty submultisets of a multiset ordered by inclusion, which corresponds to a product of chains with the bottom element deleted. We show that the total depth agrees with Stanley depth for but not for such posets in general. We also prove that the total depth of the product of chains with the bottom element deleted is , which generalizes a result of Biró, Howard, Keller, Trotter, and Young (2010). Further, we provide upper and lower bounds for a general multiset and find the total depth for any multiset with at most five distinct elements. In addition, we can determine the total depth for any multiset with distinct elements if we know all the interval partitions of . 相似文献
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We derive quantitative bounds for eigenvalues of complex perturbations of the indefinite Laplacian on the real line. Our results substantially improve existing results even for real potentials. For -potentials, we obtain optimal spectral enclosures which accommodate also embedded eigenvalues, while our result for -potentials yield sharp spectral bounds on the imaginary parts of eigenvalues of the perturbed operator for all . The sharpness of the results are demonstrated by means of explicit examples. 相似文献
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Jaewook Ahn 《Journal of Differential Equations》2019,266(10):6866-6904
A fully parabolic chemotaxis system in a smooth bounded domain , with homogeneous Neumann boundary conditions is considered, where the non-negative chemotactic sensitivity function χ satisfies , for some and . It is shown that a novel type of weight function can be applied to a weighted energy estimate for . Consequently, the range of μ for the global existence and uniform boundedness of classical solutions established by Mizukami and Yokota [23] is enlarged. Moreover, under a convexity assumption on Ω, an asymptotic Lyapunov functional is obtained and used to establish the asymptotic stability of spatially homogeneous equilibrium solutions for under a smallness assumption on μ. In particular, when and , it is shown that the spatially homogeneous steady state is a global attractor whenever . 相似文献
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Laihao Ding Guan-Huei Duh Guanghui Wang Tsai-Lien Wong Jianliang Wu Xiaowei Yu Xuding Zhu 《Discrete Mathematics》2019,342(1):279-284
A graph is -choosable if the following holds: For any list assignment which assigns to each vertex a set of real numbers, and assigns to each edge a set of real numbers, there is a total weighting such that for , and for every edge . This paper proves that if is a connected graph of maximum degree , then is -choosable. 相似文献
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For an integer , a graph is -hamiltonian if for any vertex subset with , is hamiltonian, and is -hamiltonian connected if for any vertex subset with , is hamiltonian connected. Thomassen in 1984 conjectured that every 4-connected line graph is hamiltonian (see Thomassen, 1986), and Ku?zel and Xiong in 2004 conjectured that every 4-connected line graph is hamiltonian connected (see Ryjá?ek and Vrána, 2011). In Broersma and Veldman (1987), Broersma and Veldman raised the characterization problem of -hamiltonian line graphs. In Lai and Shao (2013), it is conjectured that for , a line graph is -hamiltonian if and only if is -connected. In this paper we prove the following.(i) For an integer , the line graph of a claw-free graph is -hamiltonian if and only if is -connected.(ii) The line graph of a claw-free graph is 1-hamiltonian connected if and only if is 4-connected. 相似文献
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We consider the structure of -free subgraphs of graphs with high minimal degree. We prove that for every there exists an so that the following holds. For every graph with chromatic number from which one can delete an edge and reduce the chromatic number, and for every graph on vertices in which all degrees are at least , any subgraph of which is -free and contains the maximum number of copies of the complete graph is -colorable.We also consider several extensions for the case of a general forbidden graph of a given chromatic number, and for subgraphs maximizing the number of copies of balanced blowups of complete graphs. 相似文献
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《Discrete Mathematics》2022,345(10):112998
Let G be a graph and let f be a positive integer-valued function on . In this paper, we show that if for all , , then G has a spanning tree T containing an arbitrary given matching such that for each vertex v, , where denotes the number of components of and denotes the number of components of the induced subgraph with the vertex set S. This is an improvement of several results. Next, we prove that if for all , , then G admits a spanning closed walk passing through the edges of an arbitrary given matching meeting each vertex v at most times. This result solves a long-standing conjecture due to Jackson and Wormald (1990). 相似文献
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J. Wu 《Indagationes Mathematicae》2019,30(4):536-541
In this short note, we prove that for , where is the Euler totient function and is the integral part of real . This improves recent results of Bordellès–Heyman–Shparlinski and of Dai–Pan. 相似文献
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The paper investigates longtime dynamics of the Kirchhoff wave equation with strong damping and critical nonlinearities: , with . The well-posedness and the existence of global and exponential attractors are established, and the stability of the attractors on the perturbation parameter ? is proved for the IBVP of the equation provided that both nonlinearities and are of critical growth. 相似文献
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Let be a simple connected graph with vertices and edges. The spectral radius of is the largest eigenvalue of its adjacency matrix. In this paper, we firstly consider the effect on the spectral radius of a graph by removing a vertex, and then as an application of the result, we obtain a new sharp upper bound of which improves some known bounds: If , where is an integer, then The equality holds if and only if is a complete graph or , where is the graph obtained from by deleting some edge . 相似文献