Báo cáo toán học: " Bounded-degree graphs can have arbitrarily large slope numbers" ppsx

... Bounded-degree graphs can have arbitrarily large slope numbers J´anos Pach ∗ and D¨om¨ot¨or P´alv¨olgyi R´enyi Institute, ... (cn/d) (d−4)n/2 different graphs G R := F ∪ R, each having maximum degree at most d (here c>0 is a constant; see e.g. [BC78]). Suppose that each G R can be drawn using S slopes σ 1 < <σ S . Now we cannot ... G R , becausewedonotknowtheactual v...

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

... in ∆ n , we must have i ≤ r. Similarly, if s ≥ i, then the equation of H i requires (r −s)x r +(n−r)·1 +1 = 0, implying that x r < 0, so again x ∈ ∆ n . Therefore we must have 0 ≤ s < i ... ≤ n. Indeed, it can easily be checked that A(n, i) = (2i + 1) A(n −1, i) + (2n − 2i + 1) A(n − 1, i − 1), by examining how a signed permutation counted by the left-hand-side can arise from t...

Ngày tải lên: 07/08/2014, 06:22

... 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, into a direct sum of irreducible representation matrices of the symmetric group. 1 Introduction If G is a finite group, H is a subgroup of G and Z is a generating set of...

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 ... complete graphs into subgraphs isomorphic to a given graph, Congressus Numerantium XV (1975), 647-659. the electronic journal of combinatorics 4 (1997), #R1 5 Finally, if 1 ≤ b ≤ d then we...

Ngày tải lên: 07/08/2014, 06:20

... 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 the right side can be reduced to ≤ 6−2(i+j). For p 3 = 2 and p 3 = 4, we can thus assume p 2 ≤ 3 and p 2 ≤ 1, respectively. Only when p 3 = 2, p 2 = 2 or p 3 = 4, p 2 = 1 can equality be obtained ... planarity. For large n, the Maker/Breaker parameter τ M (NP n ) is easily seen to be bounded by a constant independent of n, since Maker can create a K 5 in a constant number of mov...

Ngày tải lên: 07/08/2014, 15:22

... show that the right 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 ... 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...

Ngày tải lên: 07/08/2014, 15:23

... Summary All the 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 , ... ori- ented bordered surfaces with marked points. We will call such graphs “of geometric type”. Besides graphs with 2 vertices, and graphs of geometric type, there are only 9 other “exc...

Ngày tải lên: 07/08/2014, 21:21