Báo cáo toán học: "A tight lower bound for convexly independent subsets of the Minkowski sums of planar point sets" potx

... whether a superlinear lower bound exists for M(n, n). The quantity M(n, n) gives an upper bound for the largest convexly independent subset of P ⊕ P, and it is related to the convex dimension of ... least the diameter of the point set P . The chain C has n + 1 vertices including two endpoints. Now we can the electronic journal of combinatorics 17 (2010),...

Ngày tải lên: 08/08/2014, 11:20

... we see that 12/ 29 is a lower bound on the density of D. The organization of the rest of the paper is as follows. In Section 2 we prove the main result. This proof consist of stating six discharging ... proof of Theorem 1. We think our proof of Theorem 1 could b e refined to give a better lower bound. However, we think t hat bound would be only slightly better t...

Ngày tải lên: 08/08/2014, 01:20

... consisting of the two degree-2 vertices in the copy of X and, if N ∗ uv = ∅, the P 1 -component consisting of the degree-2 vertex in the copy of Z, are precisely the components of G[S] minus the path-component ... cycle. The three types of units are shown in Figure 2. the electronic journal of combinatorics 14 (2007), #R65 8 the link vertex and a neighbor o...

Ngày tải lên: 07/08/2014, 15:23

Ngày tải lên: 05/08/2014, 10:20

Ngày tải lên: 05/08/2014, 10:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:20

... ≥ 1, by (11) - (12) and the definition of the Lorentz norm we get  R n   (D α f λ m )(x)v(x)   dx ≤ C α, f 1− |α|  N Φ   |β|= D β f N Φ  |α|  . (13) Therefore, using Fatou’s lemma, ... is true for all v ∈ M Φ (R n ), v M Φ ≤ 1, by the definition of · N Φ we have ||D α f|| N Φ ≤ C α, f 1− |α|  N Φ   |β|= D β f N Φ  |α|  < ∞, 0 < |α| <. The p...

Ngày tải lên: 06/08/2014, 05:20

... The lower bound on γ(G) is a stronger version of Erd¨os and Gallai’s result, and so the proof of the lower bound is a new way of proving of Erd¨os and Gallai’s result. the electronic journal of ... involved [4] ,[] . The proof of our main result (Theorem 3 in Section 4) is based on the greedy procedure. Since Theorem 3 implies Theorem 1, the proof of Theore...

Ngày tải lên: 07/08/2014, 06:20