Báo cáo toán học: "Explicit Ramsey graphs and orthonormal labelings" pdf

... is Ω(m 4/3 ). Here we improve this bound and describe an explicit construction of triangle free graphs with independence numbers m and Ω(m 3/2 ) vertices. Our graphs are Cayley graphs and their construc- tion ... Tough Ramsey graphs without short cycles, to appear. [3] N. Alon and N. Kahale, in preparation. [4] N. Alon and J. H. Spencer, The Probabilistic Method, Wiley, 19...

Ngày tải lên: 07/08/2014, 06:20

... Tanaka, Finite Euclidean graphs and Ramanujan graphs, Discrete Mathematics (to appear). [9] D. Bauer, J. Vandenheuvel and E. Schmeichel, Toughness and Triangle-Free Graphs, Journal of Combinatorial ... early version of this manuscript and the referee for helpful suggestions to improve the presentation of this paper. References [1] N. Alon, Explicit Ramsey graphs and orthon...

Ngày tải lên: 07/08/2014, 15:22

... bits and n output bits, and where the depth of the circuit is in O(log(n)). For a detailed discussion and further survey of this class of problems and their link to communication complexity and ... (and this paper provide some evidence of this) progress in under- standing and bounding guessing numbers for various natural classes of graphs is needed in order to solve some of the...

Ngày tải lên: 07/08/2014, 15:22

... subset A and B such that the induced graphs G[A] and G[B] are edge-empty and complete, respectively, and, thus, we have a contradiction by Proposition 5.1. Suppose |S|  4, and let H 1 and H 2 denote disjoint ... 10 complete graphs. 2 Notation All graphs considered in this paper are simple and finite. We let n(G) and m(G) denote the order and size of a graph G, respectiv...

Ngày tải lên: 08/08/2014, 12:22

... gain, and biased graphs. directed graph digraph • A digraph is an oriented all-positive ordinary graph. Thus, see both “Graph Structures” and “Orientation” (of signed, gain, and biased graphs) ... signed graphs. There are real, physical spin glasses, but I do not discuss them since they are not graphs. There are also features of models studied in physics, like randomness of bond s...

Ngày tải lên: 07/08/2014, 05:23

... C.C.Rousseau and R.H.Schelp, Ramsey minimal graphs for star forests, Discrete Math. 33 (1981), 227–237. [4] S.A.Burr, P.Erd˝os, R.J.Faudree, C.C.Rousseau and R.H.Schelp, Ramsey minimal graphs for ... match- ings,inThe Theory and Applications of Graphs (G.Chartrand, ed.) Wiley (1981) pp.159–168. [5] S.A.Burr, P.Erd˝os, R.J.Faudree, C.C.Rousseau and R.H.Schelp, Ramsey minima...

Ngày tải lên: 07/08/2014, 06:20

... edges. References [1] S. Brandt, Expanding graphs and Ramsey numbers, submitted. [2] S. Brandt, G. Brinkmann, T. Harmuth, The generation of maximal triangle-free graphs, submitted. [3] G. Brinkmann, All Ramsey numbers ... all Ramsey graphs and all maximal graphs needed to determine the graphs on 10 vertices with Ramsey number 19 was a bit less than 9 days on a mixed clust...

Ngày tải lên: 07/08/2014, 06:22

... Klavˇzar and R. ˇ Skrekovski, On median graphs and median grid graphs, Discrete Math. 219 (2000) 287–293. [10] S. Klavˇzar, H. M. Mulder, and R. ˇ Skrekovski, An Euler-type formula for median graphs, ... (Chapman and Hall, New York, 1993). [7] W. Imrich and S. Klavˇzar, Product Graphs: Structure and Recognition (John Wiley & Sons, New York, 2000). [8] W. Imrich, S. Klavˇz...

Ngày tải lên: 07/08/2014, 07:21

... On the Graphs of Hoffman-Singleton and Higman-Sims Paul R. Hafner Department of Mathematics University of Auckland Auckland (New Zealand) hafner@math.auckland.ac.nz Submitted: Mar ... Then u and u  have the same 3 neighbours in each of C 1 , S, and C 2 . Moreover, if z ∈ L 1 , then u and z  are adjacent if and only if u  and z are adjacent. Proof. Let w =(4, 0, 0) and consid...

Ngày tải lên: 07/08/2014, 08:22

... 3-existentially closed block intersection graphs. Both of the STS(13)s and 76 of the 80 STS(15)s violate criterion (iii) and the four other STS(15)s, #1, #2, #3 and #16 in the standard listing in [17] contain ... evidence suggests that 3-e.c. strongly regular graphs which occur as the block intersection graphs of Steiner triple systems are a rare and elusive species and likely...

Ngày tải lên: 07/08/2014, 13:21