Báo cáo toán học: "Embedding a Forest in a Graph" ppsx

... contain any point in Q as its interior point, and there is a line segment L i that intersects two nonadjacent edges of S. Case-4: The center of S is inside R ∗ ,andS contains a point in Q as its ... length of the minimum square that can contain N unit squares in the plane whose interiors do not overlap. The problem of packing unit squares into a square was initiated by Erd˝os and...

Ngày tải lên: 07/08/2014, 13:21

... a 2-fan of type 2 if and only if n = 2a( a −1), m = (a −2) (a −1 )a( a +1) and  8a( a − 1) is an integer. Now, 8a( a −1) = 1 6a( a −1)/2, and thus, if 8a( a −1) is a square, then so is a( a −1)/2isasquareaswell,buta (a ... containing four consecutive numbers is called a 3-fan. It will be shown that G × + contains 3-fans, in nitely many 2-fans and even arbitrarily large “bundles”...

Ngày tải lên: 07/08/2014, 08:20

... A j and A i  ∩ A j  = ∅. If (I) holds, then A j contains X − A i . But A j contains A i , and so A j contains X; a contradiction. Consider (II). Since A i  ∩ A j  = ∅, we have (X − A i ) ∩ A j = ... a 1 a 2 a 4 |b 1 b 4 b 5 . Similarly, by (tc), we infer a 1 a 2 a 4 |b 2 b 4 b 6 , a 1 a 3 a 4 |b 1 b 3 b 5 , a 1 a 3 a 4 |b 2 b 3 b 6 . In...

Ngày tải lên: 07/08/2014, 21:20

... a 1 , . . . , a p can be embedded in any graph containing at least  p i=1 (a i + 1) vertices and having minimum degree at least  p i=1 a i . 1 Introduction It is a folklore fact that every tree ... induction on p, the number of trees in the forest. We can assume that every tree in a forest has at least two vertices, so a i ≥ 1. The Base Case, p = 1. The forest in...

Ngày tải lên: 08/08/2014, 14:23

... 0 for all z ∈ K. The variational inequality has emerged as a fascinating and interesting branch of mathematical and engineering sciences with a wide range of applications in industry, finance, ... for all a ∈ A, then inf a A max b∈B p (a, b) = max b∈B inf a A p (a, b). Definition 2.6 (KKM mapping). Let K be a nonempty subset of a linear space E. A set-valued mapping G : K −→...

Ngày tải lên: 20/06/2014, 21:20

... LTP gain is generally limited to a certain constant to avoid the over-estimation of the pitch. Choi and Kang EURASIP Journal on Advances in Signal Processing 2011, 2011:141 http://asp.eurasipjournals.com/content/2011/1/141 Page ... estimation improves the capability of preserving speech information, However, the system delay increases somehow due to the look-ahead memory. A method to fi...

Ngày tải lên: 20/06/2014, 21:20

... high, as indicated by carbon contents that average 2-6%, but having intervals reaching values as high as 9-12% (Guardado et al., 2000). The lacustrine saline sediments of the Lagoa Feia Formation ... biodegradation of terpanes, hopanes and steranes under aerobic and anaerobic conditions, Table 3, indicate that some of the controversial biomarker parameters can be easily explained by takin...

Ngày tải lên: 20/06/2014, 21:20

... sums a+ b where a ∈ A and b ∈ B range over given sets A, B ⊆ Z/pZ of residues modulo a prime p,sothata = b. A solution was given in 1994 by Dias da Silva and Hamidoune. In 1995, Alon, Nathanson and ... A → B be an injective mapping from A to B. Suppose that m + n ≥ q +1. Then |A τ + B| >q− √ q − 1 2 . In a certain (rather narrow) range of m, n and in the particul...

Ngày tải lên: 07/08/2014, 06:20

... Richter, Separating and nonseparating disjoint homotopic cycles in graph embeddings, J. Combin. Theory Ser. B 66 (1996), 201–231. [4] S. Cabello and B. Mohar, Finding shortest non-separating and non-contractible ... of G intersected by the (dual) edges of C ∗ . Then G − F is actually a plane embedding, and we easily add the edges of F back to G − F , making a plane drawing D with at mos...

Ngày tải lên: 07/08/2014, 15:23

... which has made the question on the size of a partial spread in such a space, an intriguing question. A partial spread is said to be maximal if it cannot be extended to a larger partial spread. In ... The d ual polar graph We will consider the dual polar graph Γ, associated with a polar space P. The vertices of this graph are the generators (i.e., d-spaces in P), and two vertic...

Ngày tải lên: 07/08/2014, 21:21