Báo cáo toán học: "Bootstrap Percolation and Diffusion in Random Graphs with Given Vertex Degree" pptx

... Diffusion of innovations on random networks: Understanding the chasm. In Proceedings of WINE 2 008, pages 178–185, 2008. [20] M. Molloy and B. Reed. A critical point for random graphs with a given ... the study of percolation in a random graph with given vertex degrees. We refer to Section 3 for more details. k-Core in Random Graphs with Given Degree Seque...

Ngày tải lên: 08/08/2014, 12:22

Ngày tải lên: 05/08/2014, 15:21

... other hand, bearing in mind that µ and ν are in the interior of the same Weyl chamber C,andwµ = µ + and wν = ν + are dominant, we may use Proposition 4.4 to compare the ranks of x(µ)andx(ν) in the ... , including the cross section X and the subspace V .Moreover,V also carries a standard ordering relative to the root system Φ; however, these two “standard” orderings of V coincide:...

Ngày tải lên: 07/08/2014, 08:22

... noting that |a + b| 2 + |a − b| 2 = |a| 2 + |b| 2 and then using (2) and (1) (i.e.,  y P (x, y) = 1). The final inequality follows from (3). As an immediate consequence, we have for F satisfying ... feasible to extend such relations to directed graphs. In a directed graph, the distance and diameter can be naturally defined: The distance from a vertex u to a vertex v is the length...

Ngày tải lên: 07/08/2014, 13:21

... 5)/4, contradicting Observation 1. Hence there is no edge joining a vertex in {v 10 ,v 11 } and a vertex in {v 12 ,v 13 }. Suppose that a vertex in {v 10 ,v 11 } and a vertex in {v 12 ,v 13 } ... 4-cycle containing both v 1 and v 2 or containing both v 3 and v 4 . Proof. Suppose, to the contrary, that there is a 4-cycle containing both v 1 and v 2 or containing both...

Ngày tải lên: 07/08/2014, 13:21

... k-dominating set of G if the distance between each vertex u ∈ V − D and D is at most k (and D induces a connected graph in G). The minimum cardinality of a (connected) distance k-dominating set in ... k-dominating set of G if the distance between each vertex u ∈ V − D and D is at most k (and D induces a connected graph in G). The minimum cardinality of a (connected) distance k...

Ngày tải lên: 07/08/2014, 15:22

... maximal independent set and that in every graph, γ(G) ≤ i(G) ≤ β(G) where γ(G) and i(G) are respectively the minimum cardinality of a dominating set and of an independent dominating set and β(G) ... Hedetniemi and S. T. Hedetniemi, Alliances in graphs, JCMCC 48 (2004), 157-177. [7] N. Linial, D. Peleg, Y. Rabinovich and M. Saks, Sphere packing and local majorities in gra...

Ngày tải lên: 07/08/2014, 21:20

... After taking limits as l goes to in nity, our main result computes the heat kernel in this case. Theorem (Main Theorem). For the homesick random walk with parameter µ on the in nite line, the ... the first summand involves the eigenvalues of the Laplacian with eigenfunction not vanishing at the vertex 0 and the second the eigenvalues with the corresponding eigenfunction being z...

Ngày tải lên: 07/08/2014, 21:21

... through the edges and vertices of W n in order, traversing every edge in a straight manner and pausing for a non-trivial interval at every vertex it visits (and each time it visits that vertex) ; more ... Diestel and D. K¨uhn. On in nite cycles II. Combinatorica , 24:91–116, 2004. [15] R. Diestel and D. K¨uhn. Topological paths, cycles and spanning trees in infinite graph...

Ngày tải lên: 07/08/2014, 21:21

... 1, and 2. Thus preservation of the indices is not possible in t his case. However, it would be interesting to know when one can leave the indices invariant and this will b e investigated in the ... of the embedding factor w ′ = 343 which has embedding index 5, and the two 2’s of u are in po sitions 6 and 7. Note that we obtain ordinary factor order by taking P to be an antichain...

Ngày tải lên: 08/08/2014, 01:20