Báo cáo toán học: "Building Graphs from Colored Trees" ppsx

... find a path from (u, k) to (u, ℓ−λ ) , then by following the lifting of the path in G, there is a path from (u, ℓ − λ) to (v, ℓ). Now, assuming that k = ℓ − λ, we must find a path from (u, k) ... path from (u, k) to (w, k + κ) in G ′ . Since (w, k + κ) is in the lifting of the small cycle, we know that there is a path from (w, k + κ) to (w, ℓ − λ − κ) in G ′ . Thus, the path in G ′...

Ngày tải lên: 08/08/2014, 12:23

... the amount of flow that has to go from A to A. This amount is  v∈A α(v) −  v∈A β(v), The flow leaving A is constrained by the capacity of the cut, i.e., number of edges oriented from A to A in Z, this ... Felsner, Convex drawings of planar graphs and the order dimension of 3- polytopes, Order 18 (2001), pp. 19–37. [3] S. Felsner, Geodesic embeddings and planar graphs, Order 20 (2003),...

Ngày tải lên: 07/08/2014, 08:20

... multipartite graphs by monochromatic trees, J. Graph Theory 48 (2005), 133-141. [6] M. Kano and X. Li, Monochromatic and heterochromatic subgraphs in edge -colored graphs - a survey, Graphs and ... optimal partition in the 3-edge -colored case. We first introduce two types of graphs. Let G = K(A, B) be a 2-edge -colored complete bipartite graph, and all the edges are colored with b...

Ngày tải lên: 07/08/2014, 21:20

Ngày tải lên: 05/08/2014, 15:20

... studying the family of Cayley graphs for a given finite group G, which focuses attention on those graphs Γ for which N Aut(Γ) (G)istran- sitive on edges, and those undirected graphs Γ for which N Aut(Γ) (G) ... undirected vertex-transitive graphs with n vertices are Cayley graphs (see [5, Table 1]). ACayleygraphΓ=Cay(G, S) is said to be edge-transitive if Aut(Γ) is Cayley Graphs of...

Ngày tải lên: 06/08/2014, 05:20

... P. Erd˝os and T. Gallai, Graphs with prescribed degrees of vertices (Hungarian), Math. Lapok 11 (1960), 264-274. [10] T. Gustavsson, Decompositions of large graphs and digraphs with high minimum ... North Carolina, Chapel Hill (1970) 428-450. [21] R. M. Wilson, Decomposition of complete graphs into subgraphs isomorphic to a given graph, Congressus Numerantium XV (1975), 647-659. the ele...

Ngày tải lên: 07/08/2014, 06:20

... . (58) Finally we will derive the CUE result (44) for the ensemble of graphs defined in the previous subsection starting from the periodic-orbit expansion (45). We find K 2 (n)=  π/2 0 dµ(η)K 2 (n; ... < 1/2) (50) and find from (41) G(x)= 2x 1 −2x − 1 2 + ∞  m=0 (−1) m 2  2m m  x 2m (1 −2x) = 1 2 1 −2x √ 1+4x 2 − 1 2 1 − 6x 1 − 2x . (51) On the other hand we have from (49) G(x)= x...

Ngày tải lên: 07/08/2014, 06:23

... need to intro- duce a probability space of graphs on n vertices to make the notion of a “typical graphs ∗ Supported by a USA-Israel BSF grant, by a grant from the Israel Science Foundation and a ... random graphs, Combinatorica 17 (1997), 303–313. [2] B. Bollob´as, The chromatic number of random graphs, Combinatorica 8 (1988), 49–55. [3] T. Luczak, The chromatic number of random gra...

Ngày tải lên: 07/08/2014, 06:23

... show that every regular matroid is a HPP matroid. For graphs, Proposition 3.1 is part of the “folklore” of electrical engineering. We take it from Corollary 8.2(a) and Theorem 8.9 of [3], but include ... is at least (k +1)Ψ k+1 MS, completing the proof.  Unfortunately, it is not hard to find planar graphs which fail to satisfy the hypothesis of Proposition 4.6 in the case k = 2. An easy...

Ngày tải lên: 07/08/2014, 08:22

... volume growth. Our graph is in some sense a hybrid of the Cayley graphs of the Grigorchuk groups and the graphs from long range percolation. Like the graphs generated by long range percolation our graph ... main tools are induction and the symmetries of the graphs G k . By knowing the distance from 0 to 2 k for all k<nwe can determine the distance from 0 to 2 n . The inductiv...

Ngày tải lên: 07/08/2014, 13:21