共查询到20条相似文献,搜索用时 31 毫秒
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Let be a set of at least two vertices in a graph . A subtree of is a -Steiner tree if . Two -Steiner trees and are edge-disjoint (resp. internally vertex-disjoint) if (resp. and ). Let (resp. ) be the maximum number of edge-disjoint (resp. internally vertex-disjoint) -Steiner trees in , and let (resp. ) be the minimum (resp. ) for ranges over all -subset of . Kriesell conjectured that if for any , then . He proved that the conjecture holds for . In this paper, we give a short proof of Kriesell’s Conjecture for , and also show that (resp. ) if (resp. ) in , where . Moreover, we also study the relation between and , where is the line graph of . 相似文献
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In this paper, we show that for any fixed integers and , the star-critical Ramsey number for all sufficiently large . Furthermore, for any fixed integers and , as . 相似文献
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Michael Tait 《Discrete Mathematics》2018,341(1):104-108
Let denote that any -coloring of contains a monochromatic . The degree Ramsey number of a graph , denoted by , is . We consider degree Ramsey numbers where is a fixed even cycle. Kinnersley, Milans, and West showed that , and Kang and Perarnau showed that . Our main result is that and . Additionally, we substantially improve the lower bound for for general . 相似文献
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Tomoya Kato 《Journal of Differential Equations》2018,264(5):3402-3444
We consider the Cauchy problem for the generalized Zakharov–Kuznetsov equation on three and higher dimensions. We mainly study the local well-posedness and the small data global well-posedness in the modulation space for and . We also investigate the quartic case, i.e., . 相似文献
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Susan A. van Aardt Christoph Brause Alewyn P. Burger Marietjie Frick Arnfried Kemnitz Ingo Schiermeyer 《Discrete Mathematics》2017,340(11):2673-2677
An edge-coloured graph is called properly connected if any two vertices are connected by a path whose edges are properly coloured. The proper connection number of a connected graph denoted by , is the smallest number of colours that are needed in order to make properly connected. Our main result is the following: Let be a connected graph of order and . If , then except when and where and 相似文献
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In this paper, we consider combinatorial numbers , mentioned as Catalan triangle numbers where . These numbers unify the entries of the Catalan triangles and for appropriate values of parameters and , i.e., and . In fact, these numbers are suitable rearrangements of the known ballot numbers and some of these numbers are the well-known Catalan numbers that is .We present identities for sums (and alternating sums) of , squares and cubes of and, consequently, for and . In particular, one of these identities solves an open problem posed in Gutiérrez et al. (2008). We also give some identities between and harmonic numbers . Finally, in the last section, new open problems and identities involving are conjectured. 相似文献
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Liuquan Wang 《Discrete Mathematics》2018,341(12):3370-3384
Let be the number of -colored generalized Frobenius partitions of . We establish some infinite families of congruences for and modulo arbitrary powers of 3, which refine the results of Kolitsch. For example, for and , we prove that We give two different proofs to the congruences satisfied by . One of the proofs uses a relation between and due to Kolitsch, for which we provide a new proof in this paper. 相似文献
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A Steiner 2- trade is a pair of disjoint partial Steiner triple systems, each on the same set of points, such that each pair of points occurs in if and only if it occurs in . A Steiner 2- trade is called d-homogeneous if each point occurs in exactly d blocks of (or ). In this paper we construct minimal d-homogeneous Steiner 2- trades of foundation and volume for sufficiently large values of . (Specifically, if is divisible by 3 and otherwise.) 相似文献
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This paper considers a degree sum condition sufficient to imply the existence of vertex-disjoint cycles in a graph . For an integer , let be the smallest sum of degrees of independent vertices of . We prove that if has order at least and , with , then contains vertex-disjoint cycles. We also show that the degree sum condition on is sharp and conjecture a degree sum condition on sufficient to imply contains vertex-disjoint cycles for . 相似文献
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T. Oikhberg 《Journal of Approximation Theory》2011,163(3):311-327
For an operator , we denote by , , , and its approximation, Gelfand, Kolmogorov, and absolute numbers, respectively. We show that, for any infinite-dimensional Banach spaces and , and any sequence , there exists for which the inequality holds for every . Similar results are obtained for other -scales. 相似文献
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Stephan Fackler 《Comptes Rendus Mathematique》2013,351(1-2):53-56
In this short Note we give a self-contained example of a consistent family of holomorphic semigroups such that does not have maximal regularity for . This answers negatively the open question whether maximal regularity extrapolates from to the -scale. 相似文献
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