Báo cáo toán học: " New Bounds for Union-free Families of Sets" potx

... elements of C  2 . In case B1, at most two elements of C  2 generate the same vertex of degree zero. Since, by symmetry, one element in C  2 produces two vertices with degree zero or New Bounds for ... Lower bounds For a given finite regular graph G =(V,E), let B = |B(v)| denote the size (indepen- dent of its centre) of a ball of radius one; let C be an identifying cod...

Ngày tải lên: 07/08/2014, 06:20

... yield bounds on the size of union-free families. the electronic journal of combinatorics 5 (1998), # R39 11 4 Lower bound on f We give a construction of a (strongly) union-free family of subsets of ... ≤ 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 Coppersmith (email: co...

Ngày tải lên: 07/08/2014, 06:22

... L n . There the authors gave the following bounds for the asymp- totics of f(n), the number of forests of L n ,andα(n), the number of acyclic orienta- tions of L n :3.209912 ≤ lim n→∞ f(n) 1/n 2 ≤ ... =(V,E), a forest of G is a subset A of E that contains no cycle. A spanning forest of G is a spanning subgraph whose edge set is a forest. An acyclic orientation of G is an...

Ngày tải lên: 07/08/2014, 07:21

... ε d−1 by the choice of δ. This proves the claim. (3) The proof is similar to the proof of Claim 4.8 (2). (4) The proof is similar to the proof of Claim 4.8 (1).  the electronic journal of combinatorics ... key ingredient of our proof. Given the informal discussion above, the proof of Theorem 1.1 looks very roughly as follows. At the first part of the proof we consider the graph...

Ngày tải lên: 07/08/2014, 21:21

... below). For information about publishing your research in Journal of Inequalities and Applications go to http://www.journalofinequalitiesandapplications.com/authors/instructions/ For information ... 64p 3 + 36p 2 − 12p + 1, (2.10) 6 holds for all a, b > 0 with a = b if and only if α ≤ (1 +  16/π 2 − 1)/2 and β ≥ (3 + √ 6)/6. 2 Proof of Theorem 1.1 Proof of Theorem 1.1. Let λ...

Ngày tải lên: 20/06/2014, 21:20

... coloring of the edges of K r,r contains 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 ... 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

... ≤                                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) for r ≡ 3mod4. For the square lattice: the electronic journal of combinatorics 8 (2001), ... values of r. The square lattice with two diagonals is considered in [4] and [3]. 2 General lower bounds We conside...

Ngày tải lên: 07/08/2014, 06:22

... 153 and k 3 (8) ≥ 398. The proofs are founded on a recent technique of the author for dealing with systems of linear inequalities satisfied by the number of elements of a covering code, that lie ... the proof of Lemma 1A (with σ 1 instead of σ), we see that µ 2 ∈ C ∩ A σ 2 then cannot contribute to the 1-covering of A σ 1 despite d(σ 1 , σ 2 ) = 1. This would result in an enlar...

Ngày tải lên: 07/08/2014, 15:22

... informed by them, form the set of newly informed vertices. The concept of lazy phases was already used in [7]. They greatly simplify the analysis, but they of t en leave a constant fraction of ... performing a lazy ph a se of K rounds, we will have at least (1 − 4ζ)n newl y informed vertices with probability 1 − e −cn . The fact of having all but a constant fraction of vertices...

Ngày tải lên: 08/08/2014, 01:20

... entrywise bounds for second and lower eigenvectors of adjacency matrix of Planted partition models. We make a step towards resolving these questions through computing entrywise bounds for the second ... A. Generalizations of spectral norm bounds discussed above have been successfully used for analyzing sp ectral heuristics for the Planted partition model [5, 2, 7, 13]. The...

Ngày tải lên: 08/08/2014, 01:20