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We prove that for every fixed k and ? ≥ 5 and for sufficiently large n, every edge coloring of the hypercube Qn with k colors contains a monochromatic cycle of length 2 ?. This answers an open question of Chung. Our techniques provide also a characterization of all subgraphs H of the hypercube which are Ramsey, that is, have the property that for every k, any k‐edge coloring of a sufficiently large Qn contains a monochromatic copy of H. © 2006 Wiley Periodicals, Inc. J Graph Theory 53: 196–208, 2006 相似文献
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关于Ramsey数下界的部分结果 总被引:3,自引:1,他引:2
刘富贵 《数学的实践与认识》2002,32(1):97-99
本文得到 Ramsey数下界的一个计算公式 :R( l,s+ t-2 )≥ R( l,s) + R( l,t) -1 ,(式中 l、s、t≥ 3) .用此公式算得的 Ramsey数的下界比用其它公式算得的下界好 . 相似文献
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Mark L. Lewis 《Algebras and Representation Theory》2002,5(3):277-304
Let G be a solvable group with five character degrees. Suppose that there is some prime p so that G/O
p
(G) is not Abelian. Also, assume that cd(G) contains a degree that is not divisible by p. Under these hypotheses, we show that the derived length of G is at most 4. 相似文献
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提出了核双电荷交换反应的双重子共振态的反应机制,成功地解释了长期以来一直困惑着人们的共振区反应的角分布的实验结果.说明了共振区核双电荷交换反应是寻找双重子共振态的一个可能的途径. 相似文献
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Lingsheng Shi 《Journal of Graph Theory》2005,50(3):175-185
The Ramsey number R(G1,G2) of two graphs G1 and G2 is the least integer p so that either a graph G of order p contains a copy of G1 or its complement Gc contains a copy of G2. In 1973, Burr and Erd?s offered a total of $25 for settling the conjecture that there is a constant c = c(d) so that R(G,G)≤ c|V(G)| for all d‐degenerate graphs G, i.e., the Ramsey numbers grow linearly for d‐degenerate graphs. We show in this paper that the Ramsey numbers grow linearly for degenerate graphs versus some sparser graphs, arrangeable graphs, and crowns for example. This implies that the Ramsey numbers grow linearly for degenerate graphs versus graphs with bounded maximum degree, planar graphs, or graphs without containing any topological minor of a fixed clique, etc. © 2005 Wiley Periodicals, Inc. J Graph Theory 相似文献
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For every ?>0 and every positive integers Δ and r, there exists C=C(?,Δ,r) such that the Ramsey number, R(H,H) of any r-uniform hypergraph H with maximum degree at most Δ is at most C|V(H)|1+?. 相似文献
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A one-dimensional system of hard-rod particles with rotational-like internal degrees of freedom is considered. Particles interact with each other through the infinite-range, infinitely weak attractive Kac potential, and through a nearest-neighbor short-range potential. The latter depends also on the internal states of the interacting particles. Exact results for thermodynamic properties and for some correlation functions are obtained. It is found that the considered system exhibits several first-order transitions between phases with different rotational structure, i.e., with different ordering with respect to the internal degrees of freedom. The calculated equation of state seems to suggest that in the solutions of liquid-crystalline substances in neutral solvents there may exist regions in which the coefficient of thermal expansion is negative—an effect similar to that well known in liquid water. 相似文献