Báo cáo toán học: "Sharp threshold functions for random intersection graphs via a coupling method" potx

... journal of combinatorics 18 (2011), #P36 6 Sharp threshold functions for random intersection graphs via a coupling method. Katarzyna Rybarczyk Faculty of Mathematics and Computer Science, Adam ... p) using intermediate auxiliary random graphs. From them we can deduce the assertion of the theorem. First recall (see for example [8]) that if for some graph valued random...

Ngày tải lên: 08/08/2014, 12:23

... models of random intersection gr aphs for classifi- cation. In: M. Schwaiger, O. Opitz (Eds.), Exploratory Data Analysis in Empirical Research. Springer-Verlag, Berlin, 67–81, 2003. [6] R. van der ... degrees are also studied by some authors, see e.g. [2, 7, 8], and shown to be asymptotically Poisson distributed. In this paper, we consider a variant model of random intersection gr...

Ngày tải lên: 08/08/2014, 11:20

... 3 and the generators of the ideal I given by Lemma 2.2 form a Gr¨obner basis, then standard arguments show that the resolution (2.1) passes to gr m R/I.Inthis case, a formula analogous to that ... journal of combinatorics 10 (2003), #R36 6 Short generating functions for some semigroup algebras Graham Denham ∗ Department of Mathematics University of Western Ontario London, Ontario, Can...

Ngày tải lên: 07/08/2014, 08:20

... Kotani and T. Sunada, Jacobian tori associated with a finite graph and its abelian covering graph, Adv. in Appl. Math. 24 (2000) 89-110. [7] H. M. Stark and A. A. Terras, Zeta functions of finite graphs ... Sunada [9,10]. Hashimoto [4] treated multivariable zeta functions of bipartite graphs. Bass [2] generalized Ihara’s result on the zeta function of a regular graph to an irregula...

Ngày tải lên: 07/08/2014, 13:21

... indices in a g iven class of graphs. As for n-vertex trees, it has been shown that the path has the maximal Hosoya index and the star has the minimal Hosoya index (see [12]). Hou [14] characterized ... information available for the total number of matchings of trees, unicyclic graphs, bicyclic graphs, it is natural to consider other classes of g raphs, and the connected graphs wit...

Ngày tải lên: 08/08/2014, 12:22

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Ngày tải lên: 05/08/2014, 10:20

... University, Atlanta GA 30322 Tomasz Luczak Department of Mathematics and Computer Science 400 Dowman Drive Emory University, Atlanta GA 30322 and Department of Discrete Mathematics Faculty of Mathematics ... R.C., Smallest maximally nonhamiltonian graphs, Period. Math. Hungar. 15 (1983) 57–68. [9] Clark, L.H., Entringer, R.C., Shapiro, H.D., Smallest maximally nonhamiltonian graphs II, G...

Ngày tải lên: 07/08/2014, 13:21

... Definitio ns A quasigroup is a pair (X , ◦), where X is a set and (◦) is a binary operation on X such that the equation a ◦ x = b and y ◦ a = b a r e uniquely solvable for every pair of elements a, b ... there exists a partition Γ = {P 1 , P 2 , · · · , P r } of B such that each part P i (called parallel cla s ses) is a partition of X. A GDD is called a transversal des...

Ngày tải lên: 08/08/2014, 01:20

... is at least r. One can read Ramsey Theorem for graphs as the statement that for the family G of all graphs, r(G,n) ∼ 0.5log 2 n. Larman, Matousek, Pach, and Torocsik [15] proved that for the family ... several papers on intersection graphs of translations of a plane figure ap- peared. Akiyama, Hosono, and Urabe [2] considered f (C,k), where C is the family of intersection gra...

Ngày tải lên: 07/08/2014, 08:20

... that, for all q ∈ (1, 3), P n,⌊qn⌋ will a. a.s. contain at least linearly many copies of any given planar graph, as with P n . It was also shown that the probability that P n,⌊qn⌋ will contain an ... planar graphs have recently been the subject of much activity, and many prop- erties of the standard random planar graph P n (taken uniformly at random from the set of all planar graphs...

Ngày tải lên: 08/08/2014, 11:20