Báo cáo toán học: "The Edmonds-Gallai Decomposition for the k-Piece Packing Problem" potx

... ||f - g||(h(l)+ε). Therefore ||f - g|| ≤ h(l). This completes the proof. Now we can prove the weak convergence theorem of the iterative sequence (3.1). Zhu et al. Fixed Point Theory and Applications ... in [14-19] and the references cited therein. For example, in 2003, Chidume et al. [16] introduced the following modified Mann iteration process and got the conver- gence theorems...

Ngày tải lên: 20/06/2014, 21:20

... contains the value of γ(n, δ) for n ≤ 16, 0 ≤ δ ≤ n − 1 if the value is known, otherwise upper and lower bounds for γ(n, δ). We establish these values in Sections 2, 3 and 4. TIGHT UPPER BOUNDS FOR THE ... then there are at least 4 · 4 = 16 edges from A to B. Thus, the sum of the |A v |’s is at least 16. Since |A v |≤2 for all v ∈ B we must have |A v | =2 for all eight v i...

Ngày tải lên: 07/08/2014, 06:20

... (17) where the last equation follows from (7). The error term in the first equation holds uniformly for all real numbers x by the comments after (15) and, since | cos(ux)|≤1, the error term in the second ... error term in the second equation holds uniformly for all real numbers x by (16) as does the error term in the third equation involving the integral. Then (8), (10–...

Ngày tải lên: 07/08/2014, 06:20

... definition of δ k (n). The theorem therefore follows. In the next section we show that if k = 3 then the above theorem holds for n ≥ 6. Note that the results in this section are stated for fixed k and ... asterisks. The values given for these cases are the best known upper bounds. the electronic journal of combinatorics 7 (2000), #R58 14 Lemma 4 If there esists an (n, k, 1)...

Ngày tải lên: 07/08/2014, 06:22

... +32t − 1. Then f(n) ≥ n +32t − 1, for n ≥ n t . This completes the proof of the theorem. From the above theorem, we have lim inf n→∞ f(n) − n √ n ≥  2+ 2562 6911 , which is better than the previous ... ≤ 31t + 799). Now we define these B i ’s. These subgraphs all have a common vertex x, otherwise their vertex sets are pairwise disjoint. For 7t+1 8 ≤ i ≤ t − 742, let the subgraph...

Ngày tải lên: 07/08/2014, 06:22

... invalid in the other.) This lemma, together with the discussion preceding it, completes the proof of formula (18). We leave to the reader the task of showing that this formula reduces to formula (4) ... position for T j , then the position just left of T p has the same label as the position just right of T p . (b) If the position just right of T p is a valid position for...

Ngày tải lên: 07/08/2014, 08:20

... We will skip the indices if the graph G will be understood from the context. Note that given a minimal dominating set D of a graph G,thesets D  ,D  ,P,N and R form a partition of the vertex ... neighbor of (x, y).  The bound of the theorem is sharp, for instance consider nontrivial paths on at most 3 vertices. It would be interesting to characterize graphs for which the...

Ngày tải lên: 07/08/2014, 08:22

... denote by u R the sequence obtained from u by reversing its order. The following theorem is due to Knuth [4, Theorem D]. The differences in notation and the opposite parity of l compared the electronic ... s 2 n . (1) where b(i) is the number of times the integer i occurs in the sequence T . Note that the sum of all b(i), 1 ≤ i ≤ n,isequaltol, the length of T . 3 A simple p...

Ngày tải lên: 07/08/2014, 08:22

... with directed graphs, they stated the PPC only for undirected graphs. In 1995 Bondy [2] stated a directed version of the PPC. In [3] the PPC is stated in the language of the theory of hereditary properties ... ,H k be the components of H. Then the following hold: (a) If u ∈ V (P ) , then N H i (u) ∩ N H i (u + )=∅, for i =1, ,k. (b) If {u, v}⊆N P (H i ) for some i, then {u...

Ngày tải lên: 07/08/2014, 13:21

... Yet another reformu- lation shows that the cycle index series is also  T ∈T Z(Aut(T )), where Z(Aut(T )) is the cycle index of the automorphism group of T . The following formula for the cycle ... Labelle’s) for this formula, for which only the classical single-variable form of Lagrange inversion will be necessary; then, some immediate corrolaries are stated. Finally, the...

Ngày tải lên: 07/08/2014, 13:21