Báo cáo toán học: "The Ramsey number of diamond-matchings and loose cycles in hypergraphs" potx

... p l } and we join vertices x and the electronic journal of combinatorics 15 (2008), #R126 10 The Ramsey number of diamond-matchings and loose cycles in hypergraphs Andr´as Gy´arf´as ∗ Computer and ... [12]) and t = 2 (Alon and Frankl [1] and Gy´arf´as [13]). Next we state and prove the Ramsey- type form of our main result, it determines the exact value of...

Ngày tải lên: 07/08/2014, 21:20

... of edges. Monien and Speckenmeyer in [6] investigated the special Ramsey number r k (q), the largest number of vertices in a graph with odd girth at least 2k + 3, but not containing an independent set of size ... triangle–free graph of order n with average degree d, and indepen- dence number α(G). There has been great interest in finding good lower bounds for α(G)inte...

Ngày tải lên: 07/08/2014, 06:20

... degree of vertices of G.Then α(G) ≥  n ¯ d/2. Proof. Since G contains no 3 or 5 cycles, we have α(G) ≥ d 1 (v) (consider the neighbors of v )and (G) ≥ 1+d 2 (v) (consider v and the points at ... d k−1 (v)) 1+d 1 (v)+···+ d k (v) . Proof. Randomly label the vertices of G with a permutation of the integers from 1 to n.LetA (respectively B) be the set of vertices v of G such th...

Ngày tải lên: 07/08/2014, 06:20

... two distinct local maxima of the expression being summed, and one takes over from the other as global maximum as k increases. So it only remains to determine which of S 0 and S 1 dominates the ... and M. Shahshahani, Generating a random permutation with random transpositions, Wahr. Verw. Gebiete (1981), 159–179. [10] P. Erd˝os and J. Lehner, The distribution of the number of...

Ngày tải lên: 07/08/2014, 06:20

... the values of B i in descending order (the positions of L i , in ascending order of value), followed by those of B  i in descending order (the positions of R i , in ascending order of value), ... transposing a pair of values in the permutation; reversing the order of a block of values in the permutation; rotating a block of values (in consecutive positions)...

Ngày tải lên: 07/08/2014, 07:21

... counts ordered pairs of such matchings. We claim that this is the number of spanning 2-regular subgraphs H of G consisting of even cycles (including cycles of length 2 which are the same edge ... permutation of rows and columns A is a block diagonal matrix in which each block is a square all-1 matrix. Proof of Theorem 1.1: The square of the number of perfect matc...

Ngày tải lên: 07/08/2014, 15:22

... 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 ... diamond grid minor of size r. ✷ 3 Crossing number of projective diamond grids A set C of cycles in a graph is an I-collection if each two cycles in C hav...

Ngày tải lên: 07/08/2014, 15:23

... Radziszowski, J. Stinehour and Kung-Kuen Tse. Computation of the Ramsey Number R(W 5 , K 5 ). Bulletin of the Ins titute of Combin atoric s and its Applications, 47:53–57, 2006. [18] Y. Yuansheng and G.R.T. ... Computation of the Ramsey Number R(B 3 , K 5 ). Bulletin of the Institute of Combinatorics and its Applications, 41:71–76, 2004. [2] K. Black, D. Leven and...

Ngày tải lên: 08/08/2014, 14:23

... G bounding the face of G containing u. Then  u∈U b u is in the cycle space of G and is equal to the set (δ(U)) ∗ of edges in G dual to the edges of δ(U). Since it is in the cycle space of G, ... consists of those edges that are in an odd number of elements of E. This is the thin sum of the elements of E. The cycle space Z G of G is the smallest subset of t...

Ngày tải lên: 08/08/2014, 11:20

Ngày tải lên: 05/08/2014, 09:46