Báo cáo toán học: "A Lower Bound for Schur Numbers and Multicolor Ramsey Numbers of K3" doc

... 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 m and n ,let[ m, n ]denotetheset{ i | m ≤ i ≤ n }.AsetSof integers ... 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...

Ngày tải lên: 07/08/2014, 06:20

... 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. Bondy and U.S.R. Murty, Graph Theory ... 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] Chunhui Lai, On the si...

Ngày tải lên: 07/08/2014, 06:22

... 1 vertices. the electronic journal of combinatorics 12 (2005), #N13 2 New lower bound for multicolor Ramsey numbers for even cycles Tomasz Dzido ∗ Institute of Mathematics, University of Gda´nsk, Wita Stwosza ... especially for the simplified proof of Theorem 2. Also we would like to express our gratitude to Professor Pawel ˙ Zyli´nski for his critical reading of t...

Ngày tải lên: 07/08/2014, 08:22

... where i = r − 1 and j = c − 1. Again using the fact that λ and µ agree above row r and to the left of column c (and the definitions of r and c) we see that the only possibility for λ/µ is (r, c), ... quadrants, 1, 2, and 3, as shown in Figure 1. As before, we see that the first r − 1 rows and c − 1 columns of λ and µ agree. We consider three cases based on whether and w...

Ngày tải lên: 07/08/2014, 15:22

... class of tricyclic graphs on n vertices. In this paper, a sharp lower bound for the total number of matchings of graphs in T n is determined. 1 Introduction The total number of matchings of a ... Sharp lower bound for the total number of matchings of tricyclic graphs Shuchao Li ∗ Faculty of Mathematics and Statistics Central China Normal University Wuhan ... with...

Ngày tải lên: 08/08/2014, 12:22

... 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, NY 13346 aaron@math.colgate.edu...

Ngày tải lên: 07/08/2014, 06:23

... 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 J. Bourchier blvd, ... overview of the 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 followi...

Ngày tải lên: 07/08/2014, 13:21

... thickness of Mg is 200 Å; Mg300, thickness of Mg is 300 Å; Mg400, thickness of Mg is 400 Å. Figure 4. Dependence of reflectance on the Mg thickness and oxidation steps. Figure 5. Effect of Mg ... because of the high reflectance. To solve this problem, Mg is oxidized and MgO is formed. The reflectance of Mg is decreased dramatically after the oxidation. The reflectan...

Ngày tải lên: 20/06/2014, 21:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:20