共查询到20条相似文献,搜索用时 46 毫秒
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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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We show that if is a graph with minimum degree at least three, then and this bound is tight, where is the total domination number of , the matching number of and the path covering number of which is the minimum number of vertex disjoint paths such that every vertex belongs to a path in the cover. We show that if is a connected graph on at least six vertices, then and this bound is tight, where denotes the neighborhood total domination number of . We observe that every graph of order satisfies , and we characterize the trees achieving equality in this bound. 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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Chang-Long Yao 《Stochastic Processes and their Applications》2018,128(2):445-460
Consider (independent) first-passage percolation on the sites of the triangular lattice embedded in . Denote the passage time of the site in by , and assume that . Denote by the passage time from 0 to the halfplane , and by the passage time from 0 to the nearest site to , where . We prove that as , a.s., and Var; in probability but not a.s., and Var. This answers a question of Kesten and Zhang (1997) and improves our previous work (2014). From this result, we derive an explicit form of the central limit theorem for and . A key ingredient for the proof is the moment generating function of the conformal radii for conformal loop ensemble , given by Schramm et al. (2009). 相似文献
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We consider the number of distinct distances between two finite sets of points in , for any constant dimension , where one set consists of points on a line , and the other set consists of arbitrary points, such that no hyperplane orthogonal to and no hypercylinder having as its axis contains more than points of . The number of distinct distances between and is then Without the assumption on , there exist sets , as above, with only distinct distances between them. 相似文献
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In this article, we present a Schwarz lemma at the boundary for pluriharmonic mappings from the unit polydisk to the unit ball, which generalizes classical Schwarz lemma for bounded harmonic functions to higher dimensions. It is proved that if the pluriharmonic mapping f ∈ P(D~n, B~N) is C~(1+α) at z0 ∈ E_rD~n with f(0) = 0 and f(z_0) = ω_0∈B~N for any n,N ≥ 1, then there exist a nonnegative vector λ_f =(λ_1,0,…,λ_r,0,…,0)~T∈R~(2 n)satisfying λ_i≥1/(2~(2 n-1)) for 1 ≤ i ≤ r such that where z'_0 and w'_0 are real versions of z_0 and w_0, respectively. 相似文献
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