Báo cáo toán học: "Growth of graph powers" ppsx

... something of the form λr with λ > 1 3 . To see this, consider the following sequence of graphs H r (d) as d tends to infinity: the electronic journal of combinatorics 18 (2011), #P88 5 Growth of graph ... increase in the number of edges of the cube of a regular, co nnected graph. Such an increase was already demonstrated by Hegarty in Theorem 2. Here we give an alternative...

Ngày tải lên: 08/08/2014, 14:23

... The scheme of the catalyst preparation. Figure 2. TEM image of as-prepared CNTs. The inset shows the histogram of the diameter distribution of CNTs. Figure 3. XRD spectrum of CNTs. Figure ... number of works discussing the transition metals: molybdenum ratio and role of molybdenum in the efficient growth of CNTs with uniform diameter distribution [13-16]. A high am...

Ngày tải lên: 20/06/2014, 20:20

... of the graph G. We also establish a link between an algebraic property of the rational function (the factorization of the numerator) and a combinatorial property of the graph (the existence of ... denominator of the reduced form of Ψ P is known (Bou07). In this article, the first author has investigated the effects of elementary transformations of the Hasse diagram of a...

Ngày tải lên: 08/08/2014, 01:20

... resu lts of Farzad et al. on graphs of girth at least 7. We also make a remark on reconstruction of graphs from their higher powers. 1 Introduction For a simple, undirected, connected graph H ... H 2 the vertex v must the electronic journal of combinatorics 18 (2011), #P139 3 Uniqueness of graph square roots of girth six Anna Adamaszek ∗ Department of Computer Science and Ce...

Ngày tải lên: 08/08/2014, 14:23

... first proof of the general result. 2 Edge orientations and chip-firing For a graph G, an acyclic edg e orientation is an assignment of directions to all edges, such that the resulting digraph is ... reduced form through a series of successive deletions of pairs of letters (not necessarily adjacent). For uw k u −1 , the number of such deletions is the same as the number of letter...

Ngày tải lên: 08/08/2014, 01:20

... squares of column −59 and row 59 of Q 119 are covered, so a copy of Q 118 is dominated. the electronic journal of combinatorics 8 (2001), #R29 16 Values of Domination Numbers of the Queen’s Graph Patric ... squares of these orthogonals are not covered by the required lines for a 0-cover D of size 2k + 1 for Q 4k+1 with e = f + 2; since the set of required lines of D is s...

Ngày tải lên: 07/08/2014, 06:22

... Thenµ p (I) ≤ p. Our proof uses measure preserving homomorphisms between graphs. One of the fundamental questions first studied in extremal graph theory is the question of bounding the size of an intersecting ... importance of being biased (1.36 hardness of approximating Vertex-Cover). Annals of Mathematics,toappear.Proc. of 34th STOC, 2002. [2] P. Erd˝os, C. Ko, R. Rado, Inter...

Ngày tải lên: 07/08/2014, 13:21

... number of reaches of G M equals the algebraic and geometric multiplicity of 0 as an eigenvalue of M. Proof. Let R 1 , , R k denote the reaches of G M and let H i denote the exclusive part of R i for ... 3 Proof. Let M = D − DS be given as stated. As in the proof of Theorem 3.2 above, we may assume without loss of generality that S ii = 1 whenever D ii =0. (2) We further observ...

Ngày tải lên: 07/08/2014, 13:21

... set of limiting densities of minor-closed graph families is the topological closure of the set of densities of density-minimal graphs. Proof. By Corollary 8, the set of limiting densities of minor-closed ... from? Planar graphs, forests, outerplanar graphs, and matchings all form instances of minor- closed families of simple graphs, families of the graphs with the proper...

Ngày tải lên: 08/08/2014, 12:22

... each element of λ i is labeled with the largest label of an element of λ i−1 of smaller value. • For odd i > 1, each element of λ i is labeled with the largest label of an element of λ i−1 to ... articulation points to any or all of the other patterns. The method of proof is to s how that the elements of the latter classes can be represented as bounded merges of eleme...

Ngày tải lên: 08/08/2014, 12:22