Báo cáo toán học: "Improved Upper Bounds for Self-Avoiding Walks in Zd" ppt

... 05A15 Abstract New upper bounds for the connective constant of self-avoiding walks in a hypercubic lattice are obtained by automatic generation of finite automata for counting walks with finite memory. The upper bound ... numbers g (d,k) (n). Since a self-avoiding walk does not contain loops of any length, we can obtain an upper bound for the number f (d) (n) of self-av...

Ngày tải lên: 07/08/2014, 06:20

... 1, bound (14) is the best in all known upper bounds for G 2 , and bound (18) is the best in all known upper bounds for G 3 . Finally, bound (22) is the best upper bound for G 1 and bound (1 8) ... E(G)    . (12) In Sectio n 2, we introduce some lemmas and some new and sharp upper bounds for λ(G), which are better than all of the above mentioned upper bounds...

Ngày tải lên: 08/08/2014, 12:23

... γ(n, δ) can be reduced further by using the upper bounds given in Proposition 3.1 (taking s = 1) and Reed’s Theorem. See Table 2 for upper bounds computed using Proposition 3.1. Let Ub(n, δ) denote ... is the set N [v]=N(v)∪{v}. S ⊆ V is a dominating set for G if  x∈S N[x]=V. The domination number, γ(G), is the cardinality of a smallest dominating set for G.Ifx∼yor x = y we s...

Ngày tải lên: 07/08/2014, 06:20

... combinatorics 7 (2000), #R58 3 One easily sees that γ(n, δ) is a non-increasing function in δ. We are interested in determining the numbers δ k (n)where δ k (n)=max{δ |γ(n, δ) ≥ k},k≥ 1. Since ... −i ∈ S. See Alspach [1] for general results concerning isomorphism of circulant graphs. For each S ⊆{±1, ±2, ,±9} Fisher and Spaulding [5] obtained a formula for the domination number of t...

Ngày tải lên: 07/08/2014, 06:22

... there are many other instances of determining F -saturated graphs of minimum size. Some instances that have been considered, outside of those mentioned in the introduction, include paths and stars ... join. Determining the exact value of this function for a given graph F has been quite difficult, and is known for relatively few graphs. K´aszonyi and Tuza in [12] proved the best known ge...

Ngày tải lên: 07/08/2014, 13:21

... the upper bounds obtained by linear pro- gramming coincide with the bound µ(n, d)  n! (d−1)! of theorem 1. For 14  n  16, computations of the LP bound give n! (d−1)!  a ∗ for all d  n. In ... 1: LP bound for 11  n  13 Applying theorem 1 to the results of Table 1, we obtain recursive consequences. This leads to the upper bounds appearing in Table 2. The previous known...

Ngày tải lên: 08/08/2014, 12:22

... on a predefined criterion, which r esults in th at only a best relay is selected for NC-ing the received signals and broadcasting the NC-ed signal in BC phase. Thus, after performing NC on the ... we should consider the direct l ink. Besi des this, in Figure 5(b) it is observed that the gain of ergodic capacity obtained in direct link systems is increasing with SNR when the value of...

Ngày tải lên: 20/06/2014, 21:20

... for his useful comments and insight regarding this paper. More importantly, however, I would like to thank him for sparking my interest in combinatorics and for sharing his mathematical philosophies. The ... Bounds for Ramsey Numbers It is amazing that the result of this section has not been observed for the 25 years since [C] was published. Using this observation we will give 6...

Ngày tải lên: 07/08/2014, 06:20

... actually meet the upper bound in (2) for q odd follows from [13]. Therefore the constructions we present below are interesting mainly for k < g/2. Before proceeding, we mention that in every case ... determining v(k,g) is unsolved for most pairs (k,g) and is extremely hard in the general case. It is easy to establish the following lower bounds for v(k,g): v(k,g)≥ k(k−1) (...

Ngày tải lên: 07/08/2014, 06:22

... found. Asking for the linear combination to have strictly positive coefficients (and not just nonnegative) assures that they are, in a certain sense, stationary points of f, see [5] for more details. ... journal of combinatorics 9 (2002), #R6 8 3 Results for H 7 to H 12 Below we list the coordinates of the points of the configurations obtained by applying our method to find new bounds...

Ngày tải lên: 07/08/2014, 06:23