共查询到20条相似文献,搜索用时 15 毫秒
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《Annals of Pure and Applied Logic》2022,173(8):103135
We further develop a forcing notion known as Coding with Perfect Trees and show that this poset preserves, in a strong sense, definable P-points, definable tight MAD families and definable selective independent families. As a result, we obtain a model in which , each of , , has a witness and there is a well-order of the reals. Note that both the complexity of the witnesses of the above combinatorial cardinal characteristics, as well as the complexity of the well-order are optimal. In addition, we show that the existence of a well-order of the reals is consistent with and each of the following: , , , where the smaller cardinal characteristics have co-analytic witnesses.Our methods allow the preservation of only sufficiently definable witnesses, which significantly differs from other preservation results of this type. 相似文献
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In 2009, Kyaw proved that every -vertex connected -free graph with contains a spanning tree with at most 3 leaves. In this paper, we prove an analogue of Kyaw’s result for connected -free graphs. We show that every -vertex connected -free graph with contains a spanning tree with at most 4 leaves. Moreover, the degree sum condition “” is best possible. 相似文献
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In this article, we study the structure of finitely ramified mixed characteristic valued fields. For any two complete discrete valued fields and of mixed characteristic with perfect residue fields, we show that if the n-th residue rings are isomorphic for each , then and are isometric and isomorphic. More generally, for , there is depending only on the ramification indices of and such that any homomorphism from the -th residue ring of to the -th residue ring of can be lifted to a homomorphism between the valuation rings. Moreover, we get a functor from the category of certain principal Artinian local rings of length n to the category of certain complete discrete valuation rings of mixed characteristic with perfect residue fields, which naturally generalizes the functorial property of unramified complete discrete valuation rings. Our lifting result improves Basarab's relative completeness theorem for finitely ramified henselian valued fields, which solves a question posed by Basarab, in the case of perfect residue fields. 相似文献
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We give exact growth rates for the number of bipartite graceful permutations of the symbols that start with for (equivalently, -labelings of paths with vertices that have as a pendant label). In particular, when the growth is asymptotically like for . The number of graceful permutations of length grows at least this fast, improving on the best existing asymptotic lower bound of . Combined with existing theory, this improves the known lower bounds on the number of Hamiltonian decompositions of the complete graph and on the number of cyclic oriented triangular embeddings of and . We also give the first exponential lower bound on the number of R-sequencings of . 相似文献
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Let be the -color Ramsey number of an odd cycle of length . It is shown that for each fixed , for all sufficiently large , where is a constant. This improves an old result by Bondy and Erd?s (1973). 相似文献
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The Erd?s–Gallai Theorem states that every graph of average degree more than contains a path of order for . In this paper, we obtain a stability version of the Erd?s–Gallai Theorem in terms of minimum degree. Let be a connected graph of order and be disjoint paths of order respectively, where , , and . If the minimum degree , then except several classes of graphs for sufficiently large , which extends and strengths the results of Ali and Staton for an even path and Yuan and Nikiforov for an odd path. 相似文献
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The -additive codes are subgroups of , and can be seen as linear codes over when , -additive codes when , or -additive codes when . A -linear generalized Hadamard (GH) code is a GH code over which is the Gray map image of a -additive code. Recursive constructions of -additive GH codes of type with are known. In this paper, we generalize some known results for -linear GH codes with to any prime when , and then we compare them with the ones obtained when . First, we show for which types the corresponding -linear GH codes are nonlinear over . Then, for these codes, we compute the kernel and its dimension, which allow us to classify them completely. Moreover, by computing the rank of some of these codes, we show that, unlike -linear Hadamard codes, the -linear GH codes are not included in the family of -linear GH codes with when prime. Indeed, there are some families with infinite nonlinear -linear GH codes, where the codes are not equivalent to any -linear GH code with . 相似文献
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For given graphs , , the -color Ramsey number, denoted by , is the smallest integer such that if we arbitrarily color the edges of a complete graph of order with colors, then it always contains a monochromatic copy of colored with , for some . Let be a cycle of length and a star of order . In this paper, firstly we give a general upper bound of . In particular, for the 3-color case, we have and this bound is tight in some sense. Furthermore, we prove that for all and , and if is a prime power, then the equality holds. 相似文献
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Define a -star to be the complete bipartite graph . In a 2014 article, Hoffman and Roberts prove that a partial -star decomposition of can be embedded in a -star decomposition of where is at most if is odd and if is even. In our work, we offer a straightforward construction for embedding partial -star designs and lower these bounds to and , respectively. 相似文献
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A matching in a 3-uniform hypergraph is a set of pairwise disjoint edges. We use to denote the 3-uniform hypergraph whose vertex set can be partitioned into two vertex classes and of size and , respectively, and whose edge set consists of all the triples containing at least two vertices of . Let be a 3-uniform hypergraph of order with no isolated vertex and for any two adjacent vertices . In this paper, we show that contains a matching of size if and only if is not a subgraph of . This result improves our previous one in Zhang and Lu (2018). 相似文献
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《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
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We compute the number of (weak) equivalence classes of branched covers from a surface of genus to the sphere, with 3 branching points, degree , and local degrees over the branching points of the form , , , for several values of and . We obtain explicit formulae of arithmetic nature in terms of the local degrees . Our proofs employ a combinatorial method based on Grothendieck’s dessins d’enfant. 相似文献
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《Discrete Mathematics》2019,342(4):934-942
Fricke, Hedetniemi, Hedetniemi, and Hutson asked whether every tree with domination number has at most minimum dominating sets. Bień gave a counterexample, which allows us to construct forests with domination number and minimum dominating sets. We show that every forest with domination number has at most minimum dominating sets, and that every tree with independence number has at most maximum independent sets. 相似文献
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This paper studies the properties of -symmetric vector random fields in , whose direct/cross covariances are functions of -norm. The spectral representation and a turning bands expression of the covariance matrix function are derived for an -symmetric vector random field that is mean square continuous. We also establish an integral relationship between an -symmetric covariance matrix function and an isotropic one. In addition, a simple but efficient approach is proposed to construct the -symmetric random field in , whose univariate marginal distributions may be taken as arbitrary infinitely divisible distribution with finite variance. 相似文献