Báo cáo toán học: "Bounded-Degree Graphs have Arbitrarily Large Geometric Thickness" potx

... arbitrarily large geometric thickness. In particular, for all ∆ ≥ 9 and for all large n, there exists a ∆-regular graph with geometric thickness at least c √ ∆ ... Bounded-degree graphs can have arbi- trarily large slope numbers. Electron. J. Combin., 13:N1, 2006. [25] J ´ anos Pach and Rephael Wenger. Embedding planar graphs at fixed vertex locations. Graphs Combin., ... D...

Ngày tải lên: 07/08/2014, 13:21

... = |E(G)|/  n 2  have? In order to address this question quantitatively we need to intro- duce a probability space of graphs on n vertices to make the notion of a “typical graphs ∗ Supported ... 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 graphs,...

Ngày tải lên: 07/08/2014, 06:23

... statement, namely for bipartite graphs, was also conjectured in [5]. Several papers have app eared with proof s of Aldous’s con- jecture for some particular classes of graphs, and recently a beautiful ... Cayley graphs on the symmetric group generated by initial reversals have unit spectral gap Filippo Cesi Dipartimento di Fisica Universit`a ... Proposition 4.1]. The two largest eige...

Ngày tải lên: 07/08/2014, 21:21

... 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) ... edge-transitive Cayley graph all elements of the set S have the same order, so these graphs are not normal edge-transitive. We show that these graphs are edge-transitive. In...

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 e...

Ngày tải lên: 07/08/2014, 06:20

... determine the largest order of a graph with given degree and diameter. Many currently known largest graphs of degree ≤ 15 and diameter ≤ 10 have been found by computer search among Cayley graphs of ... graphs (not necessarily Cayley) using various voltage assignments (not necessarily satisfying the compatibility condition in case of Cayley graphs) may lead to further new examples of...

Ngày tải lên: 07/08/2014, 06:22

... family of groups whose Cayley graphs have intermediate growth [6]. See [8] for a nice description of these groups. Graphs that have intermediate volume growth also have a connection with long range percolation ... the sets H k all have density. Let d(k) be the density of H k .AsH is ω periodic we have that d(k) → 0ask →∞. Given  choose k large enough so that d(k) <. Then...

Ngày tải lên: 07/08/2014, 13:21

... and k are all odd. the electronic journal of combinatorics 14 (2007), #R32 3 Which Chessboards have a Closed Knight’s Tour within the Cube? Joe DeMaio Department of Mathematics and Statistics Kennesaw ... rectangular boards. In 1991 Schwenk [4] completely answered the question: Which rectangular chessboards have a knight’s tour? Schwenk’s Theorem: An m × n chessboard with m ≤ n has a clos...

Ngày tải lên: 07/08/2014, 15:22

... and with all (mandatory) diversity cycles involving the flexible atom is representable on arbitrarily large finite sets. Acknowledgments We thank Maria Axenovich for her valuable suggestions and ... hand side of the expression in (4) can be made less than 1 by choosing k large enough. Since 1 − x ≤ e −x for all x, we have  3k − 4 k  2 n 2  1 − 1 n 2  (k−2) 2 ≤  3k − 4 k  2 n 2  e...

Ngày tải lên: 07/08/2014, 15:23

... mutation-finite graphs from triangulations of ori- ented bordered surfaces with marked points. We will call such graphs “of geometric type”. Besides graphs with 2 vertices, and graphs of geometric ... known quivers of finite mutation type can be summarized as follows: 1. graphs of geometric type, 2. graphs with 2 vertices, 3. graphs in the 9 exceptional mutation classes E 6...

Ngày tải lên: 07/08/2014, 21:21