Báo cáo toán hoc:" Tight Bounds for Quasirandom Rumor Spreading Spyros Angelopoulos Benjamin Doerr Konstantinos Panagiotou Anna Huber" pot

... combinatorics 16 (2009), #R102 4 Tight Bounds for Quasirandom Rumor Spreading Spyros Angelopoulos Benjamin Doerr Anna Hub er Konstantinos Pana giotou Max-Planck-Institut f¨ur Informatik, 66123 Saarbr¨ucken, ... determined in [8] similar bounds for several Cayley graphs. The Quasirandom Push Model Recently, Doerr, Friedrich, and Sauerwald [7] pro- posed a quasir...

Ngày tải lên: 08/08/2014, 01:20

... 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

... (2.3) would collapse to (2.1). But this is not the case for the square grids and for the rest of this section we shall bound  ≥3 from below as tightly as we can. 2.2 Partitioning C We partition the ... 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...

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

... either a red K m,m or a green K n,n . We obtain 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 ... by T is green. Then P (R S ) = p m 2 for each of the  r m  2 choices of S, and we simply write P(R) for the common value. In the same way, P(G) = (1 − p) n 2 for each of  r n...

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 fores...

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

... 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 choices for ... exists a graph G  ∈ Γ(g) for which the following two events occur: (i) for every g  ∈ G  , {β(g  ) < β(g)}, and (ii) for every g  ∈ G  , B(T g  ,d−1 ) occurs. As before,...

Ngày tải lên: 07/08/2014, 21:21

... > n 2 , such that for every i ∈ W, v(i)  1 − β∆, where β = c 1 log n log np for some constant c 1 . A similar ar gument can be put forward using Lemmas 12 a nd 13. So, for another set Y , ... 16 (2009), #R131 16 euclidean norm for vectors and the spectral norm for matrices. For a matrix M, M ij denotes the entry in the i th row and the j th column. For a vector x ∈ R n , let...

Ngày tải lên: 08/08/2014, 01:20