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A subposet Q ′ of a poset Q is a copy of a poset P if there is a bijection f between elements of P and Q ′ such that x ≤ y in P iff f(x) ≤ f(y) in Q. For posets P, P ′, let the poset Ramsey number R(P, P ′) be the smallest N such that no matter how the elements of the Boolean lattice Q N are colored red and blue, there is a copy of P with all red elements or a copy of P ′ with all blue elements. We provide some general bounds on R(P, P ′) and focus on the situation when P and P ′ are both Boolean lattices. In addition, we give asymptotically tight bounds for the number of copies of Q n in Q N and for a multicolor version of a poset Ramsey number. 相似文献
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Maria Axenovich 《Discrete Mathematics》2006,306(18):2212-2218
How many edges can a quadrilateral-free subgraph of a hypercube have? This question was raised by Paul Erd?s about 27 years ago. His conjecture that such a subgraph asymptotically has at most half the edges of a hypercube is still unresolved. Let f(n,Cl) be the largest number of edges in a subgraph of a hypercube Qn containing no cycle of length l. It is known that f(n,Cl)=o(|E(Qn)|), when l=4k, k?2 and that . It is an open question to determine f(n,Cl) for l=4k+2, k?2. Here, we give a general upper bound for f(n,Cl) when l=4k+2 and provide a coloring of E(Qn) by four colors containing no induced monochromatic C10. 相似文献
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A code c is a covering code of X with radius r if every element of X is within Hamming distance r from at least one codeword from c. The minimum size of such a c is denoted by c
r(X). Answering a question of Hämäläinen et al. [10], we show further connections between Turán theory and constant weight covering codes. Our main tool is the theory of supersaturated hypergraphs. In particular, for n > n
0(r) we give the exact minimum number of Hamming balls of radius r required to cover a Hamming ball of radius r + 2 in {0, 1}n. We prove that c
r(B
n(0, r + 2)) = 1 i r + 1 ( (n + i – 1) / (r + 1) 2) + n / (r + 1) and that the centers of the covering balls B(x, r) can be obtained by taking all pairs in the parts of an (r + 1)-partition of the n-set and by taking the singletons in one of the parts. 相似文献
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本文叙述了在神光装置中测量激光能量的体吸收能量计的特点,给出了其工作参数。实测了神光装置中激光系统末级输出能量、激光系统前部和中部定点发射能量及激光系统放大的自发辐射能量。并作了分析和讨论。 相似文献
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单粒子气溶胶的基质辅助激光解吸/电离飞行时间质谱技术具有快速在线检测环境大气生物气溶胶的潜力.以a-环糊精为分析物,实验研究了吡啶羧酸、2,5-二羟基苯甲酸、芥子酸、阿魏酸四种常用基质材料的效果,考察基质与分析物的摩尔比对分析物单粒子激光质谱信号的影响.实验结果表明阿魏酸做基质时质谱命中率及分析物质谱信号峰检测效率最高,吡啶羧酸做基质时的分析物质谱信号峰激发率最高,信号峰强度最强.吡啶羧酸对分析物摩尔比为100:1时,分析物质谱信号检测效率最高. 相似文献
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An edge‐operation on a graph G is defined to be either the deletion of an existing edge or the addition of a nonexisting edge. Given a family of graphs , the editing distance from G to is the smallest number of edge‐operations needed to modify G into a graph from . In this article, we fix a graph H and consider Forb(n, H), the set of all graphs on n vertices that have no induced copy of H. We provide bounds for the maximum over all n‐vertex graphs G of the editing distance from G to Forb(n, H), using an invariant we call the binary chromatic number of the graph H. We give asymptotically tight bounds for that distance when H is self‐complementary and exact results for several small graphs H. © 2008 Wiley Periodicals, Inc. J Graph Theory 58:123–138, 2008 相似文献