共查询到20条相似文献,搜索用时 15 毫秒
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Hong Wang 《Graphs and Combinatorics》2010,26(6):833-877
In this paper, we prove the Erdős–Faudree’s conjecture: If G is a graph of order 4k and the minimum degree of G is at least 2k then G contains k disjoint cycles of length 4. 相似文献
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Given integers , the th power of the path is the ordered graph with vertex set and all edges of the form where . The Ramsey number is the minimum such that every 2-coloring of results in a monochromatic copy of . It is well-known that . For , Balko–Cibulka–Král–Kynčl proved that and asked for the growth rate for fixed . When , we improve this upper bound substantially by proving . Using this result, we determine the correct tower growth rate of the -uniform hypergraph Ramsey number of a -clique versus an ordered tight path. Finally, we consider an ordered version of the classical Erdős–Hajnal hypergraph Ramsey problem, improve the tower height given by the trivial upper bound, and conjecture that this tower height is optimal. 相似文献
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In 1950 P. Erdős and P. Turán published a discrepancy theorem for the zeros of a polynomial. Therein, the maximum deviation of the normalized zero counting measure from the equilibrium measure of the unit circle is estimated. Many other discrepancy theorems and related propositions about weak-star-convergence of the zero distribution of a sequence of polynomials were proved during the last decades. For several years the weak-star-convergence of the zero distribution of a sequence of rational functions is also studied. The main result of this paper is a discrepancy theorem for the zero distribution of a rational function which generalizes and sharpens previous propositions about weak-star-convergence of the zero counting measure of sequences of rational functions and known discrepancy theorems for polynomials. 相似文献
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Using undergraduate calculus, we give a direct elementary proof of a sharp Markov-type inequality \({\left\| {p'} \right\|_{\left[ { - 1,1} \right]}} \leqslant \frac{1}{2}{\left\| p \right\|_{\left[ { - 1,1} \right]}}\) for a constrained polynomial p of degree at most n, initially claimed by P. Erd?s, which is different from the one in the paper of T.Erdélyi (2015). Whereafter, we give the situations on which the equality holds. On the basis of this inequality, we study the monotone polynomial which has only real zeros all but one outside of the interval (?1, 1) and establish a new asymptotically sharp inequality. 相似文献
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Let be integers with , and set and . Because is quadratic in , there exists a such that A theorem by Erd?s states that for , any -vertex nonhamiltonian graph with minimum degree has at most edges, and for the unique sharpness example is simply the graph . Erd?s also presented a sharpness example for each .We show that if and a -connected, nonhamiltonian -vertex graph with has more than edges, then is a subgraph of . Note that whenever . 相似文献
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Let s≥2 be an integer. Denote by f 1(s) the least integer so that every integer l>f 1(s) is the sum of s distinct primes. Erd?s proved that f 1(s)<p 1+p 2+?+p s +Cslogs, where p i is the ith prime and C is an absolute constant. In this paper, we prove that f 1(s)=p 1+p 2+?+p s +(1+o(1))slogs=p 2+p 3+?+p s+1+o(slogs). This answers a question posed by P. Erd?s. 相似文献
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Based on the entropy formula for the Gauss curvature flow introduced by Bennett Chow, we define an entropy functional that is monotone along the unnormalized flow and whose critical point is a shrinking self-similar solution. 相似文献
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Given a convex body $K$ K , consider the smallest number $N$ N so that there is a point $P\in \partial K$ P ∈ ? K such that every circle centred at $P$ P intersects $\partial K$ ? K in at most $N$ N points. In 1946 Erd?s conjectured that $N=2$ N = 2 for all $K$ K , but there are convex bodies for which this is not the case. As far as we know there is no known global upper bound. We show that no convex body has $N=\infty $ N = ∞ and that there are convex bodies for which $N = 6$ N = 6 . 相似文献
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J. Korevaar 《Combinatorica》2001,21(2):239-250
Dedicated to the memory of Paul Erdős
In connection with the elementary proof of the prime number theorem, Erdős obtained a striking quadratic Tauberian theorem
for sequences. Somewhat later, Siegel indicated in a letter how a powerful "fundamental relation" could be used to simplify
the difficult combinatorial proof. Here the author presents his version of the (unpublished) Erdős–Siegel proof. Related Tauberian
results by the author are described.
Received December 20, 1999 相似文献
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YIN Linsheng 《中国科学A辑(英文版)》2000,43(8):792-794
Here we show that Rubin’s method of the use of two Euler systems to the proofs of Iwasawa main conjectures of the rational
number field and of an imaginary quadratic field is only proper to these two kinds of number fields. We mainly use the properties
of adéle ring and idéle group in class field theory to get the result. 相似文献
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М. Н. Шеремета 《Analysis Mathematica》1980,6(1):51-56
Пусть \(f(z) = \mathop \sum \limits_{k = 0}^\infty a_k z^k ,a_0 \ne 0, a_k \geqq 0 (k \geqq 0)\) — целая функци я,π n — класс обыкновен ных алгебраических мног очленов степени не вы ше \(n,a \lambda _n (f) = \mathop {\inf }\limits_{p \in \pi _n } \mathop {\sup }\limits_{x \geqq 0} |1/f(x) - 1/p(x)|\) . П. Эрдеш и А. Редди высказали пр едположение, что еслиf(z) имеет порядок ?ε(0, ∞) и $$\mathop {\lim sup}\limits_{n \to \infty } \lambda _n^{1/n} (f)< 1, TO \mathop {\lim inf}\limits_{n \to \infty } \lambda _n^{1/n} (f) > 0$$ В данной статье показ ано, что для целой функ ции $$E_\omega (z) = \mathop \sum \limits_{n = 0}^\infty \frac{{z^n }}{{\Gamma (1 + n\omega (n))}}$$ , где выполняется $$\lambda _n^{1/n} (E_\omega ) \leqq \exp \left\{ { - \frac{{\omega (n)}}{{e + 1}}} \right\}$$ , т.е. $$\mathop {\lim sup}\limits_{n \to \infty } \lambda _n^{1/n} (E_\omega ) \leqq \exp \left\{ { - \frac{1}{{\rho (e + 1)}}} \right\}< 1, a \mathop {\lim inf}\limits_{n \to \infty } \lambda _n^{1/n} (E_\omega ) = 0$$ . ФункцияE ω (z) имеет порядок ?. 相似文献
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LetH be any hypergraph in which any two edges have at most one vertex in common. We prove that one can assign non-negative real weights to the matchings ofH summing to at most |V(H)|, such that for every edge the sum of the weights of the matchings containing it is at least 1. This is a fractional form of the Erds-Faber-Lovász conjecture, which in effect asserts that such weights exist and can be chosen 0,1-valued. We also prove a similar fractional version of a conjecture of Larman, and a common generalization of the two.Supported in part by NSF grant MCS 83-01867, AFOSR Grant 0271 and a Sloan Research Fellowship 相似文献
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