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1.
What is the largest number of edges in a graph of order n and girth g? For d-regular graphs, essentially the best known answer is provided by the Moore bound. This result is extended here to cover irregular
graphs as well, yielding an affirmative answer to an old open problem ([4] p. 163, problem 10).
Received: June 27, 2000 Final version received: July 3, 2001 相似文献
2.
Bogdanovskaya V. A. Grinberg V. A. Krishtalik L. I. Kuznetsov A. M. Pleskov Yu. V. Skundin A. M. Tarasevich M. R. Tsyrlina G. A. 《Russian Journal of Electrochemistry》2003,39(4):441-444
Russian Journal of Electrochemistry - 相似文献
3.
D. Hugh Powell Andr E. Merbach Gabriel Gonzlez Ern Brücher Kroly Micskei M. Francesca Ottaviani Klaus Khler Alex Von Zelewsky Oleg Ya. Grinberg Yakob S. Lebedev 《Helvetica chimica acta》1993,76(5):2129-2146
EPR Spectra have been measured for aqueous solutions of a series of Gd3+ complexes at variable temperature and a range of magnetic fields; S-band (0.14 T), X-band (0.34 T), Q-band (1.2 T), and 2-mm-band (5.0 T). The major contribution to the observed line widths is magnetic-field-dependent and is interpreted as being due to the modulation of the zero-field splitting produced by distortion of the complexes from perfect symmetry. The transverse and longitudinal relaxation matrices for an 8S ion with such an interaction have been calculated using Redfield theory with vector-coupling methods, and diagonalised numerically to obtain relaxation rates and intensities for the degenerate transitions which contribute to the multiplet. The observed line width, which is inversely proportional to the magnetic field at low temperatures, is best described by the intensity-weighted mean transverse relaxation time for the four transitions with non-zero intensity. A least-squares fit of the data yields the square of the zero-field splitting tensor, Δ2, and a correlation time, τv, with activation energy, Ev. The physical significance of these parameters and the extent of validity of the theoretical approach are considered. The parameters are used to predict the magnetic-field dependence of the longitudinal and transverse electronic relaxation times, which are discussed in the context of their relevance to 1H-NMR relaxivity. 相似文献
4.
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
5.
Peter G. Doyle Colin Mallows Alon Orlitsky Larry Shepp 《Israel Journal of Mathematics》1989,67(1):34-42
Letn cells be arranged in a ring, or alternatively, in a row. Initially, all cells are unmarked. Sequentially, one of the unmarked
cells is chosen at random and marked until, aftern steps, each cell is marked. After thekth cell has been marked the configuration of marked cells defines some number of islands: maximal sets of adjacent marked
cells. Let ξ
k
denote the random number of islands afterk cells have been marked.
We give explicit expressions for moments of products of ξ
k
’s and for moments of products of 1/ξ
k
’s.
These are used in a companion paper to prove that if a random graph on the natural number is made by drawing an edge betweeni≧1 andj>i with probabilityλ/j, then the graph is almost surely connected ifλ>1/4 and almost surely disconnected ifλ≦1/4. 相似文献
6.
A comparison of results of indirect and direct electrochemical fluorosulfation of nonsaturated fluorocarbons shows that the main or the only product in potentiostatic conditions is vicinal fluorosulfates. Owing to a high rate of the electrochemical step, which exceeds the rate of desorption of intermediate radicals from the electrode surface into solution, it is possible to improve the process selectivity by increasing the contribution of the ionic reaction route. 相似文献
7.
Noga Alon Oded Goldreich Johan Hstad Ren Peralta 《Random Structures and Algorithms》1992,3(3):289-304
We present three alternative simple constructions of small probability spaces on n bits for which any k bits are almost independent. The number of bits used to specify a point in the sample space is (2 + o(1)) (log log n + k/2 + log k + log 1/?), where ? is the statistical difference between the distribution induced on any k bit locations and the uniform distribution. This is asymptotically comparable to the construction recently presented by Naor and Naor (our size bound is better as long as ? < 1/(k log n)). An additional advantage of our constructions is their simplicity. 相似文献
8.
Letm 3 andk 1 be two given integers. Asub-k-coloring of [n] = {1, 2,...,n} is an assignment of colors to the numbers of [n] in which each color is used at mostk times. Call an
arainbow set if no two of its elements have the same color. Thesub-k-Ramsey number sr(m, k) is defined as the minimumn such that every sub-k-coloring of [n] contains a rainbow arithmetic progression ofm terms. We prove that((k – 1)m
2/logmk) sr(m, k) O((k – 1)m
2 logmk) asm , and apply the same method to improve a previously known upper bound for a problem concerning mappings from [n] to [n] without fixed points.Research supported in part by Allon Fellowship and by a Bat Sheva de-Rothschild grant.Research supported in part by the AKA Research Fund of the Hungarian Academy of Sciences, grant No. 1-3-86-264. 相似文献
9.
As is well known, Lovász Local Lemma implies that everyd-uniformd-regular hypergraph is 2-colorable, providedd 9. We present a different proof of a slightly stronger result; everyd-uniformd-regular hypergraph is 2-colorable, providedd 8.Research supported in part by Allon Fellowship and by a grant from the United States Israel Binational Science Foundation. 相似文献
10.
Forr2 letp(n, r) denote the maximum cardinality of a subsetA ofN={1, 2,...,n} such that there are noBA and an integery with
b=y
r. It is shown that for any>0 andn>n(), (1+o(1))21/(r+1)
n
(r–1)/(r+1)p(n, r)n
+2/3 for allr5, and that for every fixedr6,p(n, r)=(1+o(1))·21/(r+1)
n
(r–1)/(r+1) asn. Letf(n, m) denote the maximum cardinality of a subsetA ofN such that there is noBA the sum of whose elements ism. It is proved that for 3n
6/3+mn
2/20 log2
n andn>n(), f(n, m)=[n/s]+s–2, wheres is the smallest integer that does not dividem. A special case of this result establishes a conjecture of Erds and Graham.Research supported in part by Allon Fellowship, by a Bat-Sheva de Rothschild Grant and by the Fund for Basic Research administered by the Israel Academy of Sciences. 相似文献