Báo cáo toán hoc:" Saturation Numbers for Trees " ppsx

... [KT86] Ta ble 2: Saturation Numbers for Trees of Order 7 Question 2: Can sharper bounds be established for Theorems 12 , 1 3, 16-19? Question 3: For those classes of trees for which the saturation ... number. Specifically, trees with long induced paths will have saturation numbers near the minimum and trees with high values for δ 2 (T ) will have high saturation...

Ngày tải lên: 08/08/2014, 01:20

... G ∪ {xy} contains a copy of H, for any two nonadjacent vertices x and y. The saturation number of H, denoted by sat(H, n), is the minimum number of edges in G for all H-saturated graphs G of ... ≥ b − 1. If exactly one of them is in B, then |N(v) ∩ N(w)| ≥ |B| − 1 = b − 1.  3 The saturation numbers for books B p Theorem 3.1 Let n and p be two positive integers such that n ≥ p 3 +...

Ngày tải lên: 07/08/2014, 21:20

... distinguish- ing numbers. Instead of asking what the distinguishing number of a fixed graph is, we may ask which distinguishing numbers are associated to a fixed group. In other words, given a group Γ we ask for ... {y 1 , ,y j } satisfies 1. φ(y i )=i for each i, 2. y i+1 is in Γ i−1 .y i for each i from 2 to j − 1, and y 1 is in Γ j−1 .y j , then j ≤ m and |Γ i−1 .y i |≥j − i + 2for...

Ngày tải lên: 07/08/2014, 08:20

... q-Euler numbers, and polynomials. 2. q-Bernoulli, q-Euler numbers and polynomials related to the Bosonic and the Fermionic p-adic integral on ℤ p In this section, we provide some basic formulas for ... and f (z)=[z + 1 2 ] k q in (2.4), respectively, we get the following formulas for the p-adic q-Bernoulli and p-adi c q-Euler numbers, respectively, if q Î ℂ p with 0 <|q -1| p <...

Ngày tải lên: 20/06/2014, 21:20

... 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 Ramsey numbers [4] have rekindled interest in this subject. ... by T is 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 ...

Ngày tải lên: 07/08/2014, 06:22

... published upper bounds. For very large numbers the improvement given by U 2,3 can be described as follows, whereweuseρ for the ratio of an upper bound to the exact value. For reasons explained in ... an upper bound (Schur, see Cor. 4), in typical cases for large a the other bounds do not give a lot of information. Of course, for such large numbers we do not know the exact value...

Ngày tải lên: 07/08/2014, 13:21

... Bielak, Size Ramsey numbers for some regular graphs, Electronic Notes in Discrete Math. 24 (2006), 39–45. [2] P. Erd˝os, R. Faudree, C. Rousseau and R. Schelp, The size Ramsey numbers, Period. Math. ... complete bipartite graph, Discrete Math. 113 (1993), 259–262. [4] I. Gorgol, On bounds for size Ramsey numbers of a complete tripartite graph, Discrete Math. 164 (1997), 149–153. the...

Ngày tải lên: 07/08/2014, 13:21

... (3.3) Therefore we are done if we can prove (3.2) for m = 1. We do this by evaluating the coefficients of a certain power series in two different ways. Lemma 1. For any positive integer p and for |z| ... congruence due to Wolstenhome, namely  2p − 1 p − 1  ≡ 1 (mod p 3 ). for primes p ≥ 5. See, e.g., [1] for this connection, and [14] for a well-known conjecture related to this. And...

Ngày tải lên: 07/08/2014, 15:23

... 5.1.4-20 of [20] for a proof. As for n(t), it is also known as the “Connes-Moscovici weight” [21]. To give a formula for it, we use the concept of the symmetry group SG ( t) of a tree. For v a vertex ... Combinatorics of root ed trees For a finite rooted tree t, we let |t| denote the number of vertices of t; T n will be the set of rooted unlabeled trees on n vertices. For examp...

Ngày tải lên: 08/08/2014, 01:20

... distributed freely for any purposes (see copyright notice below). For information about publishing your research in EURASIP WCN go to http://jwcn.eurasipjournals.com/authors/instructions/ For information ... netbooks. All this need for flexibility and more “mobile” devices lead to more and more needs to afford the spectral resources that shall be able to satisfy costumers need for mo...

Ngày tải lên: 20/06/2014, 20:20