Báo cáo toán học: "Chromatic Graphs, Ramsey Numbers and the Flexible Atom Conjecture" potx

... Sim, The normality of Cayley graphs of finite abelian groups with Valency 5, System Science and Mathematical Science 13 (2000) 420–431. Cayley Graphs of Abelian Groups Which Are Not Normal Edge-Transitive ... non- normal Cayley graphs of an abelian group are as follows. (1) G = Z 4 ,S = G\{1}, =K 4 . (2) G = Z 4 ì Z 2 = aìb,S = {a, a −1 ,b}, Γ=Q 3 the cube....

Ngày tải lên: 06/08/2014, 05:20

... solves, in particular, the related problem in Coding Theory mentioned in the introduction. the electronic journal of combinatorics 4 (1997), #R1 2 is isomorphic to H. The H -packing number of G, ... divisor of the degrees of H. Clearly, if the conditions in Wilson’s Theorem hold, then the packing and covering numbers are known. In this paper we solve all of the conjectur...

Ngày tải lên: 07/08/2014, 06:20

... properties of the set of the hook numbers for some special families of (fixed) skew -Young diagrams (Theorem1.2). The problem appeared in the study of the hook formula for various kinds of Young diagrams. ... problem appeared in the study of the hook formula for various kinds of Young diagrams. The proofs are based on properties of shifted Schur functions, due t...

Ngày tải lên: 07/08/2014, 06:20

... and the second follows from (2) and the bounds for R 5 (3) given in S. Radziszowski’s survey paper [6]. For earlier work on lower bounds for S(k) see H. Fredricksen [5] and A. Beutelspacher and W. ... D k (n)tobethemaximumofD(P )overall symmetric sum-free partitions P of [1,n]intok sets. Notethatwemusthave D k (n) ≤ S(k − 1) + 1. Symmetric Sum-Free Partitions...

Ngày tải lên: 07/08/2014, 06:20

... motivations of Odlyzko and Wilf, when they study the width of labeled trees, is to give a tight estimate for the average bandwidth of this class of tree. 2 The breadth first search random walk From ... initially (0). Then, at each of the n following stages of the BFS, the vertex x at the head of the queue is removed from the queue, and all “new” neighbor...

Ngày tải lên: 07/08/2014, 06:22

... 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

... 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

... 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

... 4 2 These are the simple roots of E 8 , which span the E 8 lattice. They correspond to the vertices v 1 , . . . , v 8 of Dyn(E 8 ), in the order shown on the right. This ordering of simple the ... reflect the structure of the underlying root system. The main examples are E 6 and E 7 . 1 Introduction The primary goal of this paper is to provide a convenient way...

Ngày tải lên: 07/08/2014, 21:20

... publication in Combinatorica. [12] M. Marciniszyn, R. Spăohel, and A. Steger. Online Ramsey games in random graphs. Accepted for publication in Combinatorics, Probability and Computing. the electronic ... bounds for online Ramsey games in random graphs. Accepted for publication in Combinatorics, Probability and Com- puting. [14] T. Măutze, R. Spăohel, and H. Thomas....

Ngày tải lên: 07/08/2014, 21:21

... such a graph G with no independent set of size at least N d k d −0.5 . the electronic journal of combinatorics 16 (2009), #R71 5 Chromatic number for a generalization of Cartesian product graphs Daniel ... of graphs. A d-fold grid over G is a graph obtained from a d-dimensional rectangular grid of vertices by placing a graph from G on each of the lines paral...

Ngày tải lên: 07/08/2014, 21:21

... Jiang, K.G. Milans, and D.B. West, Degree Ramsey number of cycles is bounded, submitted. [16] H.A. Kierstead and G. Konjevod, Coloring number and on-line Ramsey theory for graphs and hypergraphs Combin ... on-line degree Ramsey numbers for trees and cycles, draft. [18] W.B. Kinnersley, K.G. Milans, and D.B. West, Degree Ramsey numbers of graphs, submitted. [19] J. Neˇset...

Ngày tải lên: 08/08/2014, 14:23

... refine Catalan numbers and FuòCatalan numbers , by introducing colour statistics for triangulations and FuòCatalan complexes. Our renements consist in showing that the number of triangulations, respectively ... (Theorems 1.1, 1.2, 2.1, and 2.2) present renements of the plain enumeration of triangulations and FuòCatalan complexes arising from certain vertex-colourings of trian...

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

... c·ρ ( n 2 ) 1 , the electronic journal of combinatorics 18 (2011), #P158 21 q, t-Catalan numbers and generators for the radical ideal defining the diagonal locus of (C 2 ) n Kyungyong Lee ∗ Department of Mathematics University ... d ′ 2 ), and the x-coordinates of the points in D are non-negative, i.e. D ∈ D. Proof of Claim. We give the exact lower...

Ngày tải lên: 08/08/2014, 14:23