Báo cáo toán học: "Random even graphs Geoffrey Grimmett" ppt

... groups, (Z 2 ) n for example, that cannot even be generated with fewer than n =log 2 2 n elements. We begin, in Section 2, with a brief discussion of expander graphs, the representation the- ory of ... linear expanders is a family of graphs {G i | i>0}, where G i is a (n i ,d,)- expander,  and d are constants independent of n i ,andthen i tend to infinity in i. Graphs with these pr...

Ngày tải lên: 07/08/2014, 08:20

... reduced two -graphs, and let E(F) denote the class of two -graphs containing no member of F as a substructure. If f n and g n denote the numbers of labelled n-element two -graphs and reduced two -graphs ... Y unchanged.) When I speak of the pentagon and hexagon two -graphs below, I mean the two -graphs obtained from the pentagon and hexagon graphs by this procedure. All this material c...

Ngày tải lên: 07/08/2014, 06:20

Ngày tải lên: 20/06/2014, 21:20

... 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 is based on some of the ... easy; see [14]) that the independence number of G does not exceed θ(G). The graphs G n we construct here are triangle free graphs on n vertices satisfying θ(G n )=Θ(n 2/3 ), and hence the i...

Ngày tải lên: 07/08/2014, 06:20

... and lower 2-cycled graphs; these graphs are defined so that a graph is 2-cycled if and only if it is both upper 2-cycled and lower 2-cycled. In Section 4 we study the structure of 2-cycled graphs and ... of planar graphs such that a graph G canbesignedtobeα-balanced if and only if each induced subgraph of G in F can. We show here that the graphs in F areexactlythe2-connected 2-cycled...

Ngày tải lên: 07/08/2014, 06:20

... 1996 Abstract Connected graphs with minimum degree δ and at least 2δ + 1 vertices have paths with at least 2δ + 1 vertices. We provide a characterization of all such graphs which have no longer ... at least 2δ +1vertices. The complete bipartite graphs K δ,n−δ with n ≥ 2δ + 1 show that the theorem is best possible in the sense that there exist graphs of minimum degree δ with no longer...

Ngày tải lên: 07/08/2014, 06:20

... E(v, j). Since the total number of edges is fixed and each event E(v,j) “consumes” at least one edge of E, it is intuitively clear that the events E(v,j) should be negatively correlated. To prove ... all  n 2  possible edges on V , i.e. the G(n, m) model of random graphs. If n is an index running over probability spaces, we will say that a sequence of events E n occurs with high probability...

Ngày tải lên: 07/08/2014, 06:20

... recent paper of Kan- nan, Tetali and Vempala [6]: namely, randomly generating labeled bipartite graphs with a given degree sequence, and randomly generating labeled tournaments with a given score ... 1) 2 /4, (resp. n(n − 2)/4). They conjecture that this is the actual diameter of those interchange graphs. The difficulty in determining the diameter of the interchange graph (and consequently a...

Ngày tải lên: 07/08/2014, 06:20

... n 2 log n steps are enough whereas for G = Z 6 or Z 10 we only know that n 4 log n are enough. Even in the case of Z 6 it does not seem easy to improve this.” Our main contribution in this note ... knowing (or estimating) the value of α, which if anything is harder to estimate than λ 1 for general graphs. We can bypass this difficulty to some extent by the following (companion) comparison th...

Ngày tải lên: 07/08/2014, 06:22

... vertices exists which is an automorphism of G. Cayley graphs, and in particular, circulant graphs have been studied intensively in the literature. These graphs are easily seen to be vertex transitive. ... In the case of a prime vertex number n circulant graphs are known to be the only vertex transitive graphs. Because of their high symmetry, Cayley graphs are ideal models for commu-...

Ngày tải lên: 07/08/2014, 06:22