Báo cáo toán học: "Information flows, graphs and their guessing numbers" pptx

... class (of signed, gain, or bidirected graphs) Notation: [], [], [B] ã An equivalence class of signed, gain, or bidirected graphs under switching. 27 isomorphism (of signed, gain, or bidirected graphs) Notation: = ã ... signing of the underlying graph. Equiva- lent to being additively biased. signed gain graph signed graph with gains Notation: (Γ,σ,ϕ), (Φ,σ), (,) ã A...

Ngày tải lên: 07/08/2014, 05:23

... 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

... δ). We establish these values in Sections 2, 3 and 4. TIGHT UPPER BOUNDS FOR THE DOMINATION NUMBERS OF GRAPHS WITH GIVEN ORDER AND MINIMUM DEGREE W. Edwin Clark University of South Florida Tampa, ... y.IfA⊆V then we let A denote the subgraph of G induced by A. Table 1 contains the value of γ(n, δ) for n ≤ 16, 0 ≤ δ ≤ n − 1 if the value is known, ot...

Ngày tải lên: 07/08/2014, 06:20

... graph of order n with domination number at least 3 and minimum degree δ satisfying n −2 √ n −4 ≤ δ ≤ n − √ 2 √ n. Tight Upper Bounds for the Domination Numbers of Graphs with Given Order and Minimum ... combinatorics 7 (2000), #R58 19 [2] W. Edwin Clark and Larry A. Dunning, Tight Upper Bounds for the Domination Numbers of Graphs with...

Ngày tải lên: 07/08/2014, 06:22

... coloured differently. The upper and lower chromatic numbers ¯χ, χ are the maximum and minimum numbers of colours for which there exists a colouring using all the colours. The concepts of mixed hypergraph, upper and ... =3or χ =2. the electronic journal of combinatorics 8 (2001), #R6 7 On the upper and lower chromatic numbers of BSQSs(16) ∗ Giova...

Ngày tải lên: 07/08/2014, 06:22

... . the electronic journal of combinatorics 10 (2003), #R3 5 Proof. The proof is by induction on the number of vertices of a graph. The n -cube Q n , n ≥ 1, can be obtained as the expansion of the ... graphs U e and derive c (s+1) (G, −1) =  e∈F(G) θ s (U e )=θ s+1 (G). the electronic journal of combinatorics 10 (2003), #R3 8 The cube polynomial and its...

Ngày tải lên: 07/08/2014, 07:21

... same family of maximum cocliques of X and hence there exists an automorphism of Z mapping X to Y . Proof. The statement of the lemma gives sufficient indication of the proof. We note that the lemma ... The subgraph of order 80 induced by four of these subgraphs W i is identified as the second orbit of the stabiliser of the remaining one of these graphs in...

Ngày tải lên: 07/08/2014, 08:22

... an n -existentially closed graph is (n − 1) -existentially closed, the theorem is trivially true for v = 7 and 9. There are two non-isomorphic STS(13)s and 80 non- isomorphic STS(15)s, [17], and ... systems and configurations. 2 Steiner triple systems A Steiner triple system of order v, STS(v), is a pair (V, B) where V is a set of cardinality v of elements, or points, and...

Ngày tải lên: 07/08/2014, 13:21

... Decompositions of graphs into 5-cycles and other small graphs Teresa Sousa ∗ Tepper School of Business Carnegie Mellon University Pittsburgh, PA 15213 tmj@andrew.cmu.edu Submitted: ... non-complete graphs of order 4 and single edges. Let H be one of the following graphs. Theorem 2.4. Any graph of order n,withn ≥ 4, can be decomposed into at most  n 2 4  copie...

Ngày tải lên: 07/08/2014, 13:21

... one of the bicliques in B.Thebiclique cover number, bc(G), of a graph G is the minimum number of bicliques in a biclique cover of G.Abiclique partition of a graph G is a collection B of bicliques ... above and the other is K(R G ì S H ,S G ì R H ). A biclique of G ì H which is one of the two bicliques produced from the weak product of a biclique of G and a bicli...

Ngày tải lên: 07/08/2014, 13:21

... spectral radius of a general (not necessarily regular) graph G and that of a subgraph of G, see [16]. 2 The spectral radius and the maximum degree The following theorem is the main result of this ... to the extreme entries of the principal eigenvector of an irregular graph G, then one can improve the result of Theorem 2.1. However, there are infini...

Ngày tải lên: 07/08/2014, 15:22

... d(G π , s) ≥ n − k(G, s) and therefore d(G π , s) > n/2 for n ≥ 4d 2 (4d + 3). ♣ the electronic journal of combinatorics 14 (2007), #R44 16 Information flows, graphs and their guessing numbers Søren ... 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...

Ngày tải lên: 07/08/2014, 15:22

... Section 2 we construct our main tools to study the Erd˝os problem over finite Euclidean and non -Euclidean spaces, the finite Eu- clidean and non -Euclidean graphs. Our construction follows one of Bannai, ... concise, we will restrict our discussion to the finite non- Euclidean graphs obtained from the action of the simple orthogonal group on the set of non-isotropic p...

Ngày tải lên: 07/08/2014, 15:22

... 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, respectively. The path, the cycle and the complete ... 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...

Ngày tải lên: 08/08/2014, 12:22

... Lehman matrices are the thin Lehman matrices and the point-line incidence matrices of nondegenerate finite projective planes. We would like to know if there are any other infinite families of Lehman ... finite nondegenerate projective planes, a widely studied topic [4], and thin Lehman matrices. Thin Lehman matrices were defined and studied by Cornu´ejols et al. [3]. the...

Ngày tải lên: 08/08/2014, 12:23