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111.
112.
Judith Egan 《组合设计杂志》2011,19(4):304-312
In a latin square of order n , a k ‐plex is a selection of kn entries in which each row, column, and symbol occurs k times. A 1 ‐plex is also called a transversal. A k ‐plex is indivisible if it contains no c ‐plex for 0 < c < k . We prove that, for all n ≥ 4 , there exists a latin square of order n that can be partitioned into an indivisible ? n / 2 ?‐plex and a disjoint indivisible ? n / 2 ?‐plex. For all n ≥ 3 , we prove that there exists a latin square of order n with two disjoint indivisible ? n / 2 ?‐plexes. We also give a short new proof that, for all odd n ≥ 5 , there exists a latin square of order n with at least one entry not in any transversal. Such latin squares have no orthogonal mate. Copyright © 2011 Wiley Periodicals, Inc. J Combin Designs 19:304‐312, 2011 相似文献
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Xiangfei Ni 《代数通讯》2013,41(7):2433-2447
In this article, we explore the multiplicative quasi-adequate transversals of an abundant semigroup. Let S be an abundant semigroup with multiplicative quasi-adequate transversals. Then the product of any two multiplicative quasi-adequate transversals is also a multiplicative quasi-adequate transversal. Moreover, all multiplicative quasi-adequate transversals of S form a rectangular band. Let S°and S ? be multiplicative quasi-adequate transversals of S, and let δ°(δ?) be the δ-relation on S°(S ?). Then there exists a bijection ? from S°/δ°onto S ?/δ?. In particular, if δ°and δ? are congruences, then the bijection ? is an isomorphism. 相似文献
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设H=(V,E)是以V为顶点集, E为(超)边集的超图. 如果H的每条边均含有k个顶点, 则称H是k-一致超图. 超图H的点子集T称为它的一个横贯, 如果T 与H 的每条边均相交. 超图H的全横贯是指它的一个横贯T, 并且T还满足如下性质: T中每个顶点均至少有一个邻点在T中. H 的全横贯数定义为H 的最小全横贯所含顶点的数目, 记作\tau_{t}(H). 对于整数k\geq 2, 令b_{k}=\sup_{H\in{\mathscr{H}}_{k}}\frac{\tau_{t}(H)}{n_{H}+m_{H}}, 其中n_H=|V|, m_H=|E|, {\mathscr{H}}_{k} 表示无孤立点和孤立边以及多重边的k-一致超图类. 最近, Bujt\'as和Henning等证明了如下结果: b_{2}=\frac{2}{5}, b_{3}=\frac{1}{3}, b_{4}=\frac{2}{7}; 当k\geq 5 时, 有b_{k}\leq \frac{2}{7}以及b_{6}\leq \frac{1}{4}; 当k\geq 7 时, b_{k}\leq \frac{2}{9}. 证明了对5-一致超图, b_{5}\leq \frac{4}{15}, 从而改进了当k=5 时b_k的上界. 相似文献
117.
《Journal of Graph Theory》2018,88(1):174-191
We consider (not necessarily proper) colorings of the vertices of a graph where every color is thoroughly dispersed, that is, appears in every open neighborhood. Equivalently, every color is a total dominating set. We define as the maximum number of colors in such a coloring and as the fractional version thereof. In particular, we show that every claw‐free graph with minimum degree at least two has and this is best possible. For planar graphs, we show that every triangular disc has and this is best possible, and that every planar graph has and this is best possible, while we conjecture that every planar triangulation has . Further, although there are arbitrarily large examples of connected, cubic graphs with , we show that for a connected cubic graph . We also consider the related concepts in hypergraphs. 相似文献
118.
In this paper, a complete congruence on the congruence lattice of regular semigroups with Q-inverse transversals is analysed. The classes of this complete congruence which are intervals are discussed and their least and greatest elements are presented clearly. 相似文献
119.
N. Yagi N. Ohta T. Matsuo T. Tanaka Y. Terada H. Kamasaka K. To‐o T. Kometani T. Kuriki 《Journal of synchrotron radiation》2009,16(3):398-404
Early caries lesion is a demineralization process that takes place in the top 0.1 mm layer of tooth enamel. In this study, X‐ray microbeam diffraction was used to evaluate the hydroxyapatite crystallites in the subsurface lesion of a bovine enamel section and the results are compared with those obtained by transversal microradiography, a method commonly used for evaluation of tooth mineral. Synchrotron radiation from SPring‐8 was used to obtain a microbeam with a diameter of 6 µm. Wide‐angle X‐ray diffraction reports the amount of hydroxyapatite crystals, and small‐angle X‐ray scattering reports that of voids in crystallites. All three methods showed a marked decrease in the enamel density in the subsurface region after demineralization. As these diffraction methods provide structural information in the nanometre range, they are useful for investigating the mechanism of the mineral loss in early caries lesion at a nanometre level. 相似文献
120.
We present an O(mn) algorithm to determine whether a graph G with m edges and n vertices has an odd cycle transversal of order at most k, for any fixed k. We also obtain an algorithm that determines, in the same time, whether a graph has a half integral packing of odd cycles of weight k. 相似文献