Báo cáo toán học: " Lower Bounds on van der Waerden Numbers: Randomized- and Deterministic-Constructive" pdf

... combinatorics 18 (2011), #P64 5 Lower Bounds on van der Waerden Numbers: Randomized- and Deterministic-Constructive Willia m Gasarch Department of Computer Science University of Maryland at College Park College ... called nonconstructive in contrast to constructive pr oofs that provide an efficient algorithm. This paper clarifies these notions and gives d efi nitions for deter...

Ngày tải lên: 08/08/2014, 14:22

... 13 2.2 Current bounds of Van der Waerden numbers Only five smaller Van der Waerden numbers are known at present. The known Van der Waerden numbers, as well as the best known lower bounds and their ... Conclusions In this paper we presented a method to construct lower bounds for Van der Waerden numbers. The final results are shown in table 4. Table 4: Known V...

Ngày tải lên: 07/08/2014, 15:22

... (1993) 1–8. 4. W. Li, On the property of solutions of M-matrix equations, Systems Science and Math. S cience 10 (1997) 129–132. The Bounds on Comp onents of the Solution for Consistent Linear Systems ... nucleus K of A on one hand. On the other hand, in Theorem 2.4 and Corollary 2.5 we need not to assume that A is nonsingular. Hence from the fact that each principal submatrix of...

Ngày tải lên: 06/08/2014, 05:20

... ˜w 4 ˜w 5 ˜w 6 ˜w 7 ,itmustbe that m = 3 and the subword to the left of the leftmost 6 in w contains two 0’s, two 1’s, and two 2’s. However, w 1 must consist of 0 and 1 in some order, and w 2 of 1 and 2, so the two ... 1)’s in w m , one must be on the left half of s m and hence before the m in h m+1 ,and the other must be on the right half of s k−1 and hence after the k −...

Ngày tải lên: 07/08/2014, 08:20

... 1) and limit the degree of irregularity of its solutions (Lemma 2). In section 3 we start with some preliminaries. Section 4 contains a proof of k 3 (7) ≥ 155. The more detailed considerations needed ... postponed to the next section. The reader interested in this bound should keep track about some consequences of assumed equality in (13) throughout this and the previous section. These co...

Ngày tải lên: 07/08/2014, 15:22

... above lower bounds trivially imply similar lower bounds on the expectation of e(M n (H)). It is worth mentioning that all of the above lower bounds on the expectation of e(M n (H)) can be derived ... Janson, T. Luczak, and A. Ruci´nski, Random graphs, 2000. [8] S. Janson, Poisson approximation for large deviations, Random Struct. Algorithms 1 (1990), 221–230. [9] D. Osthus...

Ngày tải lên: 07/08/2014, 21:21

... m for 1  i  q and player T chooses one of the sets. Then player P chooses a second partition with the sam e properties and again player T chooses one of the sets. This goes on until player ... and covering radius R. For a monograph on covering codes see [2]. An updated table of bounds on K q (n, R) is published online by K´eri [5]. An easy lower bound on K q (n, R) is the...

Ngày tải lên: 08/08/2014, 01:20

... direction, we will only count the number of ones in rows corresponding to vertices in Q m−r . There can be at most K of these rows that conta in a single one and at most P m of these rows which contain ... Daniel W. Cranston and Gexin Yu. A new lower bound on the density of vertex identifying codes for the infinite hexagonal grid. Electron. J. Co mbin., 16(1):R113, 2009. [5] Iiro Honka...

Ngày tải lên: 08/08/2014, 12:22

... a rotation system on G and R ′ be a rota t io n system on G ′ . Let Γ and Γ ′ be the sets of rotation system on G and G ′ respectively. We denote Γ R ′ the set of all rotation systems on G that ... Science Foundation of China under Grant No. 10901048. References [1] D. Archdeacon, Calculations on the average genus and genus distribution of graphs, Congr. Numer. 67 (1988) 114...

Ngày tải lên: 08/08/2014, 12:23

... 2: A rotational Hamilton cycle in L 3 (bold). on ℓ j if and only if α i , α j and α j+1 are linearly dependent in V . Assuming this condition holds, it is clear t hat α i+1 , α j+1 and α j+2 are ... p i lies on a line ℓ j , then p i+1 lies on ℓ j+1 . A key observation is that p i lies the electronic journal of combinatorics 16 (2009), #N19 6 A note on edge-colourings avoiding ra...

Ngày tải lên: 07/08/2014, 21:21