Báo cáo toán học: "Nonexistence of graphs with cyclic defect" pot

... called cyclic defect’. Here we prove that this conjecture holds. Keywords: Graphs with cyclic defect, Moore bound, defect, repeat. 1 Nonexistence of graphs with cyclic defect Let G be a graph of ... electronic journal of combinatorics 18 (2011), #P71 4 Nonexistence of graphs with cyclic defect Mirka Miller ∗† School of Electrical Engineering and Comp. Science, Uni...

Ngày tải lên: 08/08/2014, 14:22

... (2006) Nonexistence of positive solutions of an integral system with weights Zhengce Zhang School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China Email ... monotonic- ity of the positive solutions for a class of integral systems with weights. We use a new type of moving plane method introduced by Chen–Li–Ou. Our new ingredi...

Ngày tải lên: 20/06/2014, 21:20

... complete. Nonexistence of positive solutions of an integral system with weights Zhengce Zhang School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China Email ... monotonic- ity of the positive solutions for a class of integral systems with weights. We use a new type of moving plane method introduced by Chen–Li–Ou. Our new ingr...

Ngày tải lên: 20/06/2014, 21:20

... ∂Ω. Therefore, the problem admits only the null solution. Proof Similar to the proof of theorem 1. theorem 3.3 If u k ∈ W 1,p k (x) 0 (Ω) ∩L ∞  Ω  solution of the system (1.6) −(1.7), Ω is a star shaped ... identities (2.5) and (2.6). The rest of the proof is similar to the that of lemma 1. 3 Principal Result theorem 3.1 If u ∈ W 1,p(x) 0 (Ω) ∩ L ∞  Ω  be a solution of the probl...

Ngày tải lên: 20/06/2014, 21:20

Ngày tải lên: 05/08/2014, 15:21

... G is the union of copies of K δ+1 with vertex v in common. Proof: i) Since G has no cut vertex, Theorem 4 of [3] assures us that there is a cycle of at least 2δ vertices. Let C, with vertices ... graphs. For a graph G with n vertices we define f(G) to be the number of vertices in a longest path of G, and for a vertex v of G we define f(v) to be the number of vertices in...

Ngày tải lên: 07/08/2014, 06:20

... number of k-partitions of V is k n , (5) implies that the expected number of k-colorings of G,form = cn,isoforder  k  k − 1 k  c  n . Hence, if c> ln k ln k−ln(k−1) the expected number of ... evolution of random graphs, Publication of the Mathematical Institute of the Hungarian Academy of Sciences, 5 (1960), 17–61. [6] E. Friedgut, Necessary and sufficient conditions f...

Ngày tải lên: 07/08/2014, 06:20

... electronic journal of combinatorics 10 (2003), #R40 10 Asymptotics of Permutations with Nearly Periodic Patterns of Rises and Falls Edward A. Bender Department of Mathematics University of California, ... of permutations with pattern (ud) a/2 u(ud) (b+1)/2 .Hecompares this with E n , the number of alternating permutations of the same length n = 1 a 21 b . On the other...

Ngày tải lên: 07/08/2014, 08:20

... C n .Thechromatic number of G is denoted by χ(G). Let be a family of graphs. An -decomposition of G is a set of subgraphs G 1 , ,G t such that any edge of G is an edge of exactly one of G 1 , ,G t and ... cases of graphs H of order 4 and 5 with chromatic number 3, namely C 5 , C 5 with a chord and the two connected non-bipartite non-complete graphs on 4 vertices. Th...

Ngày tải lên: 07/08/2014, 13:21

... The set of degrees of terms of f 2 is S = {2n, 2n + 4, 2n + 8, . . . , 2n + 8}. When  is even, S consists of 2+1 consecutive multiples of 4. Since n is odd, 2n is not a multiple of 8, ... > 1. The set of degrees of terms of f −1 is S = {n − n, n − n + 4, n − n + 8, . . . , n − n + 4 − 4}. Since  ≡ 1 (mod 4), the set S consists of  consecutive multiples...

Ngày tải lên: 07/08/2014, 13:21