Báo cáo toán học: "Outerplanar Crossing Numbers, the Circular Arrangement Problem and Isoperimetric Functions" doc

... Article Extension of Oppenheim’s Problem to Bessel Functions ´ Arp ´ ad Baricz and Ling Zhu Received 10 September 2007; Accepted 22 October 2007 Recommended by Andrea Laforgia Our aim is to extend some ... analogue of (1.1) is the following result. Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2007, Article ID 82038, 7 pages doi:10.1155/...

Ngày tải lên: 22/06/2014, 06:20

... class="bi x0 y0 w1 h 1" alt =""

Ngày tải lên: 05/08/2014, 15:21

... ∈ D 4 (f) then the sequence splits. Proof. Since E ∈ D 4 (f) andL f (α, ) ∈ D 3 (f) (see Proposition 2.11 in [1 ]) then (E,L f (α, )) ∈ S (see Proposition 2.9 in [1 ]). Then by Lemma 1.7 in [1] there ... ν( 2) = max((k, j),m( 2)) . Next we apply ( 4) to k =2,j = ν( 2) and choose ν( 3) = max((k, j),m( 3)) . Continuing this way and by putting a nk = a...

Ngày tải lên: 06/08/2014, 05:20

... is one of the outstanding conjectures of graph theory. the electronic journal of combinatorics 9 (2002), #R37 2 Graph Color Extensions: When Hadwiger’s Conjecture and Embeddings Help Michael O. ... K 5 and so is 4-colorable by (the proven case of) Hadwiger’s Conjecture with k =5. Wetakea 4-coloring of G  ,sayc, using the colors {1, 2, 3, 4} and transfer it to G[V − P ]...

Ngày tải lên: 07/08/2014, 07:21

... several counting problems on the square lattice L n . There the authors gave the following bounds for the asymp- totics of f(n), the number of forests of L n ,and (n), the number of acyclic orienta- tions ... y>0andz t y =1. the electronic journal of combinatorics 10 (2003), #R4 15 Improved bounds for the number of forests and acyclic...

Ngày tải lên: 07/08/2014, 07:21

... definitions of mock theta functions and their order the reader is referred to [6]. The object of this paper is to provide new number theoretic interpretations of the following mock theta functions: Ψ(q)= ∞  m=1 q m 2 (q; ... aq n+i ) , for any constant a. We remark that Ψ(q) is of order 3 while the remaining three are of order 5. Number theoretic interpretations of...

Ngày tải lên: 07/08/2014, 08:20

... his thesis the circular arrangement problem for the hypercube, and Bezrukov and Schroeder [1], who showed that for trees the solutions for the linear arrangement problem and the circular arrangement ... bound for the usual linear arrangement problem. Recall that the linear arrangement problem requires the placement of the vertices of the graph in...

Ngày tải lên: 07/08/2014, 08:22

... with n = 7 and s = 27 and get 8k 5 + 15k 6 + 22k 7 + 29  i 8 k i ≤ 58. (8) Multiplication with 3/22 and rounding off yields Lemma 3. the electronic journal of combinatorics 14 (20 07) , #R 27 4 5 ... we show k 3 (7) ≥ 156 and k 3 (8) ≥ 402 improving on the best previously known bounds k 3 (7) ≥ 153 and k 3 (8) ≥ 3 98. The proofs are founded on a recent technique...

Ngày tải lên: 07/08/2014, 15:22

... classes of patterns of size 6 the electronic journal of combinatorics 16 (20 09), #R58 7 Wilf-equivalence on k-ary words, compositions, and parking functions V´ıt Jel´ınek ∗ Department of Applied ... also consider analogous problems with in the set of integer comp ositions and the set of parking functions, which may both be regarded as special types of words, and which co...

Ngày tải lên: 07/08/2014, 21:21

... for connected graphs. Computations up to 12 vertices have shown that these graphs have the same zeta function. Czarneski also gave an example o f a pair of graphs with the same zeta function but differing ... Introduction and Statement of Results In this paper we study properties of graphs which are determined by the Ihara zeta function. Here, we allow multiple...

Ngày tải lên: 08/08/2014, 01:20

... 90C46 Abstract We consider the problem to decomp ose a binary matrix into a small number of binary matrices whose 1-entries form a r ectangle. We show that the linear relaxation of this problem has an ... points on the vertical line the electronic journal of combinatorics 16 (2009), #R89 12 A dual of the rectangle-segmentation problem for binary...

Ngày tải lên: 08/08/2014, 01:20

... such a polygon do not change genus of such a surface. Operation 1: Aaa − ∼ A, Operation 2: AabBab ∼ AcBc, Operation 3: AB ∼ {(Aa), (a − B)}, A A a a A B a b b a A B c c A B A Bc c Figure 4: Operation ... attaching ears serially or by bar -amalgamation of a cactus to G N The authors of [5] discussed a Kuratowski type theorem for average genus of graph...

Ngày tải lên: 08/08/2014, 12:23

... counterexamples to the Alon-Saks-Seymour Conjecture and to the Rank-Coloring Conjecture. We computed the eigenvalues of the adjacency matr ices of these graphs and obtained tight bounds for the ... fixed k ≥ 2 and r ≥ 1 and n larg e enough, the graphs G(n, k, r) are counterexamples to both the Alon-Saks-Seymour Conjecture and the Rank-Coloring Conjec...

Ngày tải lên: 08/08/2014, 12:23

... theorem and other identities. The proofs are “hybrid” in the sense that we use partition arguments to prove a restricted version of the theorem, and then use analytic methods (in the form of the ... 2}, {15}, the electronic journal of combinatorics 18 (2011), #P60 15 Hybrid Proofs of the q-Binomial Theorem and other identities Dennis Eichhorn Depart...

Ngày tải lên: 08/08/2014, 14:22

... partially for convenience, some assumptions are made about the connectivity of G which are not made in this note. For related work on the critical group of a line graph for an undirected graph, see ... for a careful reading and helpful com- ments. References [1] Andrew Berget, Andrew Manion, Molly Maxwell, Aaron Potechin, and Victor Reiner. The critical group of...

Ngày tải lên: 08/08/2014, 14:23