Báo cáo toán học: "New lower bound for multicolor Ramsey numbers for even cycle" doc

... Classification: 05D10 Abstract We give two lower bound formulas for multicolored Ramsey numbers. These formu- las improve the bounds for several small multicolored Ramsey numbers. 1. INTRODUCTION In this ... New Lower Bound Formulas for Multicolored Ramsey Numbers Aaron Robertson Department of Mathematics Colgate University, Hamilton, ... INTRODUCTION In this short art...

Ngày tải lên: 07/08/2014, 06:23

... We refer the reader to [6] for a survey. 2 The Ramsey numbers for even cycles Up to now, there have been known only two exact values for 3-color Ramsey numbers for even cycles. More precisely, ... Moreover, by using upper bound for Ramsey number for even cycles ([5, Section 5.7, Theorem 10]), we have R 3 (C 8 ) ≤ 2412, and by using known upper bound for Rams...

Ngày tải lên: 07/08/2014, 08:22

... published bounds for S (5) are 157 ≤ S (5) ≤ 321, the lower bound was proved in [4] and the upper bound in [6]. For Ramsey numbers we know R 2 (3) = 6 and R 3 (3) = 17; the current bounds on R 4 (3) ... 1994; Accepted: September 18, 1994 Abstract For k ≥ 5, we establish new lower bounds on the Schur numbers S(k) and on the k-color Ramsey numbers of K 3 . For integers...

Ngày tải lên: 07/08/2014, 06:20

... Lower Bounds for Ramsey Numbers It is amazing that the result of this section has not been observed for the 25 years since [C] was published. Using this observation we will give 6 new lower bounds. Currently ... 87-95. [R] S. Radziszowski, Small Ramsey Numbers, Electronic Journal of Combinatorics, Dynamic Survey DS1, 1994, 28pp. [S] Song En Min, New Lower Bound Formulas fo...

Ngày tải lên: 07/08/2014, 06:20

... Zhangzhou Teachers College(Natural Science Edition) 3(1)(1989) 55-59. [4] Chunhui Lai, Upper bound and lower bound of f(n), J. Zhangzhou Teachers Col- lege(Natural Science Edition) 4(1)(1990) 29,30-34. [5] ... Acknowledgment The author thanks Prof. Yair Caro and Raphael Yuster for sending reference [7]. The author also thanks Prof. Cheng Zhao for his advice. References [1] J.A. Bond...

Ngày tải lên: 07/08/2014, 06:22

... determination of optimal values and lower bounds for every H n . Besides the trivial cases H 3 and H 4 , Golberg showed constructions providing lower bounds for n ≤ 15. A.W.M. Dress, Yang Lu, ... value for H 5 .Theyalso improved the lower bound for H 7 . In this note, and by using a simple implementation of simulated annealing and a further optimization procedure, we present n...

Ngày tải lên: 07/08/2014, 06:23

... results about the numbers F (a 1 , ,a r ; m − 1) was given in [1]. Here we shall note only the general bounds for the numbers F (a 1 , ,a r ; m − 1). In [8] the following lower bound was proved F ... New upper bound for a class of vertex Folkman numbers N. Kolev Department of Algebra Faculty of Mathematics and Informatics “St. Kl. Ohridski” University of Sofia 5 ... [4],[6],[7]...

Ngày tải lên: 07/08/2014, 13:21

... sharp lower bound for the Hosoya index of quasi-tree graphs; see [20]. Liu and Lu characterized t he cacti graphs with minimal Hosoya index in [23]. Machnicka et al. determined sharp bounds for ... with maximal Hosoya index. For n-vertex bicyclic graphs, Deng [7, 8] determined sharp upper and lower bounds on Hosoya index of bicyclic graphs, resp ectively. Recently, for other cla...

Ngày tải lên: 08/08/2014, 12:22

... new bounds for multicolor Ramsey numbers are proved: R(K 3 ,K 3 ,C 4 ,C 4 ) ≥ 27 and R 4 (C 4 ) ≤ 19. 1 Introduction We prove two new bounds for multicolor Ramsey numbers, a lower bound for R(K 3 ,K 3 ,C 4 ,C 4 ) ... for R(K 3 ,K 3 ,C 4 ,C 4 ) by coloring K 26 , and an upper bound for R 4 (C 4 ) by a density argu- ment. 2 The Ramsey number R(K 3 ,K 3 ,C 4 ,C 4 ) F...

Ngày tải lên: 07/08/2014, 08:22

... upon acceptance. It can be downloaded, printed and distributed freely for any purposes (see copyright notice below). For information about publishing your research in Journal of Inequalities and ... article as it appeared upon acceptance. Fully formatted PDF and full text (HTML) versions will be made available soon. New proofs of Schur-concavity for a class of symmetric functions Journa...

Ngày tải lên: 20/06/2014, 21:20