Báo cáo toán học: "The Bipartite Ramsey Numbers b(C2m; K2,2)" pot

... for domination numbers of the queen’s graph, to appear in Discrete Math. [19] W. D. Weakley, A lower bound for domination numbers of the queen’s graph, submitted. the electronic journal of combinatorics ... like the ones described here. Type A 0-cover of size 2k +1 for Q 4k+1 with e = f +2. Here the required row numbers and column numbers are the members o...

Ngày tải lên: 07/08/2014, 06:22

... using the strategy outlined in the proof of Theorem 2. The length of w is larger than the number of representatives of ≡ (5k−8) classes (since it contains all of them) which is greater than Tower(k), ... of {A, B} of fixed length occur almost surely in the encoding of some interval of C n,p . In Section 5.1.2 we show that there are w ∈{A, B} ∗ that can be distinguished from a...

Ngày tải lên: 07/08/2014, 06:23

... consecutive NE pairs, is the generalized Runyon number, R m n,k = 1 n  n k  mn k − 1  . the electronic journal of combinatorics 12 (2005), #R53 3 The Generalized Schrăoder Theory Chunwei Song Dept ... higher dimensional Schrăoder theory. We introduce and derive results about the m-Schrăoder paths and words. 2 m-Schrăoder Paths and m-Schrăoder Number Now lets introduce the notions...

Ngày tải lên: 07/08/2014, 13:21

... On some Ramsey and Tur´an-type numbers for paths and cycles Tomasz Dzido Institute of Mathematics, University of Gda´nsk Wita Stwosza 57, 80-952 Gda´nsk, Poland tdz@math.univ.gda.pl Marek Kubale Algorithms ... is a path of length 3 joining x and y. Now we will show that any path of length at least 3 but shorter than k − 2 which joins x and y can be extended by two addition...

Ngày tải lên: 07/08/2014, 13:21

... Theorem 10 makes it clear that the problem of factoring the generalized zeta function is really a problem of factoring the zeta function of a bipartite graph. Fortunately, in [11], Hashimoto deals with this ... instead. 3.1. Consequences of the Factorization Our first observation is that the zeta function of a hypergraph is a non-trivial gener- alization of the...

Ngày tải lên: 07/08/2014, 13:21

... ∞. The second natural question is whether or not we can determine AR(H; b). The first question is answered in [1] by construction, which yields a partial answer to the second. Definition 1. For ... same color, exactly one such edge can be used, implying C v (R) contains a vertex corresponding to one in L(H  ), a contradiction.! Now, let T 0 = T , i = 0, and if T i contains a leaf v i with ......

Ngày tải lên: 07/08/2014, 15:23

... several properties of a maximal IC-coloring f of K m,n . Proposition 3.3. If f is a maximal IC-coloring of G = (A, B) = K m,n , then all the colorings of vertices of G are distinct. Proof. Suppose, ... proof is complete. the electronic journal of combinatorics 15 (2008), #R43 2 n ≥ 3, we have f 4 = 10 ≤ 3 · 2 4−2 − 2 4−(n+2) − 1. This is a contradiction to that f is a maximal I...

Ngày tải lên: 07/08/2014, 15:23

... 2 and k = 3. An interesting open problem is whether equality holds for all values of k. the electronic journal of combinatorics 15 (2008), #R49 2 Chromatic Graphs, Ramsey Numbers and the Flexible Atom ... L 3 and those edge colorings of K N which are good with respect to these subsets M. We also remark on the connections of these subsets and colorings to projective pl...

Ngày tải lên: 07/08/2014, 15:23

... 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

... electronic journal of combinatorics 16 (2009), #R15 8 The complexity of constructing gerechte designs E. R. Vaughan School of Mathematical Sciences, Queen Mary, University of London, UK e.vaughan@qmul.ac.uk Submitted: ... specialisation of latin squares. A gerechte skeleton of order n is an n ì n array whose n 2 cells are partitioned into n regions containing n cells each...

Ngày tải lên: 07/08/2014, 21:21

... also define CR( R n,d ) to be the maximum of the maximum rectilinear crossing numbers throughout the class of graphs. The maximum crossing number and maximum rectilinear crossing number have been studied ... proposition. the electronic journal of combinatorics 16 (2009), #R54 13 The Maximum of the Maximum Rectilinear Crossing Numbers of...

Ngày tải lên: 07/08/2014, 21:21

... Henning, Bipartite Ramsey numbers, Utilitas Math. 53 (1998) 217–230. [5] J. H. Hattingh, M. A. Henning, Star-path bipartite Ramsey numbers, Discrete Math. 185 (1998) 255–258. [6] R. W. Irving, A bipartite ... K 1,n and K 2,n − K 2,n bipartite Ramsey numbers, Discrete Math. 223 (2000) 83–92. [3] R. J. Faudree, R. H. Schelp, Path-path Ramsey- type numb ers f or the complete b...

Ngày tải lên: 08/08/2014, 12:23

... -dimensional Fibonacci cube. We give bounds on the Fibonacci dimension of a graph in terms of the isometric and lattice dimension, provide a combinatorial characterization of the Fibonacci dimension ... University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia; Faculty of Natural Sciences and Mathematics, University of Maribor, Koroˇska 160, 2000 Maribor, Slov...

Ngày tải lên: 08/08/2014, 14:22

... R(K m − P 3 , K n ; k) and v ∈ V (F ) then F [N F (v)] ∈ R(K m−1 −P 3 , K n ; d F (v)) and F[N F (v)] ∈ R(K m −P 3 , K n−1 ; k−1 −d F (v)). Thus ∆(F ) ≤ r(K m−1 − P 3 , K n ) − 1 and δ(F ) ≥ k − ... d(u 3 ) − d G[A i ] (u 1 ) − d G[A i ] (u 2 ) − d G[A i ] (u 3 ) ≤ d(u) + 11 + 11 − 2 − 2 − 2 = d(u) + 16, hence d(u) = 11. On the other hand, 27 = 39 −...

Ngày tải lên: 08/08/2014, 14:23

... On some Ramsey numbers for quadrilaterals Janusz Dybizba´nski Tomasz Dzido Institute of Informatics University of Gda´nsk, Poland jdybiz@inf.ug.edu.pl, ... computer methods we improve lower and upper bounds for some other multicolor Ramsey numbers involving q uadrilateral C 4 . We consider 3 and 4-color numbers, our results improve known bounds. 1 Introduction In ... Small R...

Ngày tải lên: 08/08/2014, 14:23