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81.
82.
Given two graphsH andG, letH(G) denote the number of subgraphs ofG isomorphic toH. We prove that ifH is a bipartite graph with a one-factor, then for every triangle-free graphG withn verticesH(G) H(T
2(n)), whereT
2(n) denotes the complete bipartite graph ofn vertices whose colour classes are as equal as possible. We also prove that ifK is a completet-partite graph ofm vertices,r > t, n max(m, r – 1), then there exists a complete (r – 1)-partite graphG* withn vertices such thatK(G) K(G*) holds for everyK
r
-free graphG withn vertices. In particular, in the class of allK
r
-free graphs withn vertices the complete balanced (r – 1)-partite graphT
r–1(n) has the largest number of subgraphs isomorphic toK
t
(t < r),C
4,K
2,3. These generalize some theorems of Turán, Erdös and Sauer.Dedicated to Paul Turán on his 80th Birthday 相似文献
83.
Summary The paper deals with the behaviour of the so-called algorithms with respect to interval filling sequences A connection is established between the uniquely representable points and the continuity points of the algorithms; also strong continuity properties on monotonic algorithms are proved. Finally the results are applied to additive functions. The theorems extend some former results by the authors, by I. Kátai and by A. Járai.Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth 相似文献
84.
In Korchmáros et al. (2018)one-factorizations of the complete graph are constructed for with any odd prime power such that either or . The arithmetic restriction is due to the fact that the vertices of in the construction are the points of a conic in the finite plane of order . Here we work on the Euclidean plane and describe an analogous construction where the role of is taken by a regular -gon. This allows us to remove the above constraints and construct one-factorizations of for every even . 相似文献
85.
András Gyárfás 《组合设计杂志》2015,23(8):321-327
A cross‐free set of size m in a Steiner triple system is three pairwise disjoint m‐element subsets such that no intersects all the three ‐s. We conjecture that for every admissible n there is an STS(n) with a cross‐free set of size which if true, is best possible. We prove this conjecture for the case , constructing an STS containing a cross‐free set of size 6k. We note that some of the 3‐bichromatic STSs, constructed by Colbourn, Dinitz, and Rosa, have cross‐free sets of size close to 6k (but cannot have size exactly 6k). The constructed STS shows that equality is possible for in the following result: in every 3‐coloring of the blocks of any Steiner triple system STS(n) there is a monochromatic connected component of size at least (we conjecture that equality holds for every admissible n). The analog problem can be asked for r‐colorings as well, if and is a prime power, we show that the answer is the same as in case of complete graphs: in every r‐coloring of the blocks of any STS(n), there is a monochromatic connected component with at least points, and this is sharp for infinitely many n. 相似文献
86.
Auer Peter Dósa György Dulai Tibor Fügenschuh Armin Näser Peggy Ortner Ronald Werner-Stark Ágnes 《Central European Journal of Operations Research》2021,29(3):1079-1113
Central European Journal of Operations Research - We deal with a very complex and hard scheduling problem. Two types of products are processed by a heterogeneous resource set, where resources have... 相似文献
87.
Dedicated to the memory of Paul Erdős
A graph is called -free if it contains no cycle of length four as an induced subgraph. We prove that if a -free graph has n vertices and at least edges then it has a complete subgraph of vertices, where depends only on . We also give estimates on and show that a similar result does not hold for H-free graphs––unless H is an induced subgraph of . The best value of is determined for chordal graphs.
Received October 25, 1999
RID="*"
ID="*" Supported by OTKA grant T029074.
RID="**"
ID="**" Supported by TKI grant stochastics@TUB and by OTKA grant T026203. 相似文献
88.
In this paper, based on theorems for limit distributions of empirical power processes for the i.i.d. case and for the case
with independent triangular arrays of random variables, we prove limit theorems for U- and V-statistics determined by generalized
polynomial kernel functions. We also show that under some natural conditions the limit distributions can be represented as
functionals on the limit process of the normed empirical power process. We consider the one-sample case, as well as multi-sample
cases.
Dedicated to Professor V. M. Zolotarev on his sixty-fifth birthday.
Supported by the Hungarian National Foundation for Scientific Research (grant No. T1666).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I. 相似文献
89.
Let \({f(x)=(x-a_1)\cdots (x-a_m)}\), where a 1, . . . , a m are distinct rational integers. In 1908 Schur raised the question whether f(x) ± 1 is irreducible over the rationals. One year later he asked whether \({(f(x))^{2^k}+1}\) is irreducible for every k ≥ 1. In 1919 Pólya proved that if \({P(x)\in\mathbb{Z}[x]}\) is of degree m and there are m rational integer values a for which 0 < |P(a)| < 2?N N! where \({N=\lceil m/2\rceil}\), then P(x) is irreducible. A great number of authors have published results of Schur-type or Pólya-type afterwards. Our paper contains various extensions, generalizations and improvements of results from the literature. To indicate some of them, in Theorem 3.1 a Pólya-type result is established when the ground ring is the ring of integers of an arbitrary imaginary quadratic number field. In Theorem 4.1 we describe the form of the factors of polynomials of the shape h(x) f(x) + c, where h(x) is a polynomial and c is a constant such that |c| is small with respect to the degree of h(x) f(x). We obtain irreducibility results for polynomials of the form g(f(x)) where g(x) is a monic irreducible polynomial of degree ≤ 3 or of CM-type. Besides elementary arguments we apply methods and results from algebraic number theory, interpolation theory and diophantine approximation. 相似文献
90.
In this paper a proposal is put forward for the calculation of the shearing factor NS linked to the well known, demagnetization coefficient ND, from the data of a sheared saturation loop, obtained by a non-toroidal, open circuit hysteresis measurement. Following that, the paper illustrates the way to recover the real static loop data from an open circuit, measured data. The proposal is based on the hyperbolic model. The proposed method was illustrated on the tests carried out on two closed and open toroidal samples, mimicking the demagnetization effect of the open circuit VSM measurement, made of NO Fe–Si electrical steel sheets. These test results, presented here, agree very well with the calculated results, based on the hyperbolic modeling. 相似文献