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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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Let and denote the maximum degree and the Laplacian spectral radius of a tree , respectively. In this paper we prove that for two trees and on vertices, if and , then , and the bound “” is the best possible. We also prove that for two trees and on vertices with perfect matchings, if and , then . 相似文献
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For bipartite graphs , the bipartite Ramsey number is the least positive integer so that any coloring of the edges of with colors will result in a copy of in the th color for some . In this paper, our main focus will be to bound the following numbers: and for all for and for Furthermore, we will also show that these mentioned bounds are generally better than the bounds obtained by using the best known Zarankiewicz-type result. 相似文献
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A -way Latin trade of volume is a collection of partial Latin squares , containing exactly the same filled cells, such that, if cell is filled, it contains a different entry in each of the partial Latin squares, and such that row in each of the partial Latin squares contains, set-wise, the same symbols, and column likewise. It is called a -way-homogeneous Latin trade if, in each row and each column, , for , contains exactly elements, and each element appears in exactly times. It is also denoted as a Latin trade, where is the size of the partial Latin squares.We introduce some general constructions for -way -homogeneous Latin trades, and specifically show that, for all , , and , and for all , (except for four specific values), a -way -homogeneous Latin trade of volume exists. We also show that there is no Latin trade and there is no Latin trade. Finally, we present general results on the existence of -way -homogeneous Latin trades for some modulo classes of . 相似文献
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Denis S. Krotov 《Discrete Mathematics》2017,340(12):2723-2731
A subspace bitrade of type is a pair of two disjoint nonempty collections of -dimensional subspaces of a -dimensional space over the finite field of order such that every -dimensional subspace of is covered by the same number of subspaces from and . In a previous paper, the minimum cardinality of a subspace bitrade was established. We generalize that result by showing that for admissible , , and , the minimum cardinality of a subspace bitrade does not depend on . An example of a minimum bitrade is represented using generator matrices in the reduced echelon form. For , the uniqueness of a minimum bitrade is proved. 相似文献
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Elena Rubei 《Discrete Mathematics》2012,312(19):2872-2880
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TextFor any given two positive integers and , and any set A of nonnegative integers, let denote the number of solutions of the equation with . In this paper, we determine all pairs of positive integers for which there exists a set such that for all . We also pose several problems for further research.VideoFor a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=EnezEsJl0OY. 相似文献
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We say a graph is -colorable with of ’s and of ’s if may be partitioned into independent sets and sets whose induced graphs have maximum degree at most . The maximum average degree, , of a graph is the maximum average degree over all subgraphs of . In this note, for nonnegative integers , we show that if , then is -colorable. 相似文献
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Sergey V. Astashkin Pavel A. Terekhin 《Journal of Mathematical Analysis and Applications》2018,457(1):645-671
Let be a mean zero function and let , , be the dyadic dilations and translations of f. We investigate conditions on f, under which the linear operator defined by , , where , , are mean zero Haar functions, can be continuously extended to the closed linear span in a certain function space X. Among other results we prove that is bounded in every symmetric space with nontrivial Boyd indices whenever and f has “good” Haar spectral properties. In the special case of so-called Haar chaoses the above results can be essentially refined and sharpened. In particular, we find necessary and sufficient conditions, under which the operator , generated by a Haar chaos f of order 1, is continuously invertible in for all . 相似文献
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Kiyoshi Ando 《Discrete Mathematics》2018,341(11):3003-3009
An edge of a -connected graph is said to be -contractible if the contraction of the edge results in a -connected graph. If every -connected graph with no -contractible edge has either or as a subgraph, then an unordered pair of graphs is said to be a forbidden pair for -contractible edges. We prove that is a forbidden pair for 6-contractible edges, which is an extension of a previous result due to Ando and Kawarabayashi. 相似文献