Báo cáo toán học: "Asymptotic Bounds for Bipartite Ramsey Numbers" pot

... asymptotic bounds for b (m, n ) for m ≥ 2 fixed and n → ∞. 1 Introduction Recent exact results for bipartite Ramsey numbers [4] have rekindled interest in this subject. The bipartite Ramsey number ... Asymptotic Bounds for Bipartite Ramsey Numbers Yair Caro Department of Mathematics University of Haifa - Oranim Tivon ... The following variation was considered by Beineke...

Ngày tải lên: 07/08/2014, 06:22

... 145–161. [3] P. Erd˝os and C. Rousseau, The size Ramsey number of a complete bipartite graph, Discrete Math. 113 (1993), 259–262. [4] I. Gorgol, On bounds for size Ramsey numbers of a complete tripartite ... ∞. References [1] H. Bielak, Size Ramsey numbers for some regular graphs, Electronic Notes in Discrete Math. 24 (2006), 39–45. [2] P. Erd˝os, R. Faudree, C. Rousseau and R....

Ngày tải lên: 07/08/2014, 13:21

... convex combination bounds of Seiffert and geometric means for the arithmetic mean. J. Math. Inequal. 5(3), 429–434 (2011) [8] Liu, H, Meng, X-J: The optimal convex combination bounds for the Seiffert’s ... particular, many remarkable inequalities and properties for T and S can be found in the literature [1–14]. 2 [6] Wang, M-K, Qiu, Y-F, Chu, Y-M: Sharp bounds for Seiffert means in...

Ngày tải lên: 20/06/2014, 21:20

... third element in its I-set. The same is true for f1andg1, or h2andh3, according to which place you choose for covering g2. Actually, the only way for c  ∈ C  to have degree exactly two is given ... incidence relation between C  and L ≥ 3 For any vertex v,letR(v) be the set of points at Euclidean distance either 2 or √ 5 from v. Now let us consider the bipartite graph Γ whose set...

Ngày tải lên: 07/08/2014, 06:20

... →∞,h(x i )→H(2p i − p 2 i ). Therefore we have [2α − β(p)+o(1)]n ≤ n  i=1 H(2p i − p 2 i ) ≤ nφ(p) (since pn =  p i ). Therefore αn ≤ 1 2 [β(p)+φ(p)+o(1)]n. New Bounds for Union-free Families of Sets Don ... D  is forced. The total number of choices on this triplet is 3 × 1 ×1 × 1+3×2×2×1=15. Values on the last triplet are forced. (Because we want an upper bound, we can ignore the chan...

Ngày tải lên: 07/08/2014, 06:22

... D(G S ,r) ≤          2 5r for r even, 2r 5r 2 − 2r +1 for r odd. For the triangular lattice: 2 6r +3 ≤ D(G T ,r) ≤          1 2r +4 for r ≡ 0mod4, 1 2r +2 for r ≡ 1, 2or3 mod4. When ... ≤                                8r − 8 9r 2 − 16r for r ≡ 0mod4, 8 9r − 25 for r ≡ 1mod4, 8 9r − 34 for r ≡ 2mod4, 8r − 16 (r − 3)(9r − 43) fo...

Ngày tải lên: 07/08/2014, 06:22

... before, the evaluation of the Tutte polynomial at these points is #P-hard for planar bipartite graphs [11] and even for grid graphs of maximum degree 3 [12]. The approach for obtaining the bounds ... polynomial contains much information on the graph G; we refer to [7] and the survey paper [3] for background information. In particular: • T(G;2, 1) is the number f(G) of spanning for...

Ngày tải lên: 07/08/2014, 07:21

... Lower bounds for the football pool problem for 7 and 8 matches Wolfgang Haas Albert-Ludwigs-Universit¨at Mathematisches ... L ≥i =  j≥i L j for i ≥ 0. (4) For λ ∈ F n 3 we define h k (λ) ∈ F k 3 (1 ≤ k ≤ n) by h k (λ) = (x 1 , , x k ) if λ = (x 1 , , x k , , x n ). Now assume C ⊂ F n 3 is a ternary code. For σ ∈ F k 3 (1 ... {σ ∈ F k 3 : n σ = i} for i = 0, 1, B = B 0 ∪ B 1 and...

Ngày tải lên: 07/08/2014, 15:22

... edges in M n (H), for H that is regular, strictly 2-balanced. As a corollary, we obtain new lower bounds for Tur´an numbers of complete, balanced bipartite graphs. Namely, for fixed r ≥ 5, we ... S for j ∈ [d − 1]. We count the number of choices for G j : There are O(d) possible choices for an edge g ∈ {f} ∪  i<j G i for which G j is in Λ(g, 1); There are at most n v H −2...

Ngày tải lên: 07/08/2014, 21:21

... phase. This means that only the newly informed vertices from the previous phase inform, and all vertices, which become informed by them, form the set of newly informed vertices. The concept of lazy ... that become informed during the current phase and do not inform any other vertices are called newly informed in this phase. In lazy phases we will assume that the action of all nodes that becom...

Ngày tải lên: 08/08/2014, 01:20