the notion of a random graph

... and B Sudakov Ramsey games with giants To appear in Random Structures Algorithms [4] T Bohman, A Frieze, and N Wormald Avoidance of a giant component in half the edge set of a random graph Random ... has average degree at most 2r (the k-core of a graph G is the maximal subgraph of G with minimum degree at least k) For some details, see the introduction of [11] It is known [15] that a. a.s the ... graph Then the theorem states that a. a.s a linear-sized ‘giant component’ emerges quite precisely at the point where the average degree in the graph is In the past decades, much research has...

Ngày tải lên: 08/08/2014, 12:22

... Annals of Mathematics, 162 (2005), 1335–1351 The two possible values of the chromatic number of a random graph By Dimitris Achlioptas and Assaf Naor* Abstract Given d ∈ (0, ∞) let kd be the ... inequality: for any nonnegative random variable X, Pr[X > 0] ≥ (EX)2 /EX THE CHROMATIC NUMBER OF A RANDOM GRAPH 1337 Specifically, the number of k-colorings of a random graph is the sum, over all ... This lemma is a variant of the classical Laplace method of asymptotic analysis in the case of the Birkhoff polytope Bk , i.e., the set of all k × k doubly stochastic matrices For a matrix A ∈ Bk...

Ngày tải lên: 29/03/2014, 07:20

... 3-SAT formulas From the set of legal colorings of a graph, Dunne and Zito singled out the special colorings that satisfy a maximality condition that, however, is a weaker form of maximality than ... main tool in establishing sharp estimates of the occupancy probabilities mentioned above, i.e the probabilities that no bin remains empty after the random placement of the balls Theorem (Kamath, ... set the accuracy parameter equal to 10−50 and set the scale of the problem equal to 10−50 Finally, we set the number of decimal digits parameter of Maple equal to 100 We run the algorithm and...

Ngày tải lên: 07/08/2014, 06:20

... its drawbacks as we shall see; it is the main reason why a two point concentration (rather than a far more desirable one point concentration) will be obtained at the end of this section The problem ... NP-complete, and since very little appears to have been done in the area of domination for random graphs (see, e.g., [4] in addition to [3],[5].) Two Point Concentration For r ≥ 1, let the random variable ... of a random graph enjoys as sharp a concentration as does its chromatic number χ [1] In Section 2, we prove this fact for the sequence of graphs {G(n, pn }, n → ∞, where a two point concentration...

Ngày tải lên: 07/08/2014, 06:22

... generalisation of the notion of a stable set Recall that a set of vertices S of a graph G is stable if no two of its vertices are adjacent In other words, the maximum degree of G[S] is 0, and therefore ... of G is the maximum order of a t-stable set in G The main topic of this paper is to give a precise formula for the t-stability number of a dense random graph The notion of a t-stable set is a ... number c of a random graph In Random Graphs ’87 (Pozna´ , 1987), pages 175–187 Wiley, n Chichester, 1990 [20] D W Matula On the complete subgraphs of a random graph In Proceedings of the 2nd Chapel...

Ngày tải lên: 08/08/2014, 12:22

... formula for the number of labelled a random graphs Eur J Comb (1980), 311 - 316 [6] B Bollob´s The evolution of sparse random graphs Graph Theory and Combinaa torics Proc Cambridge Combinatorial ... as the underlying multigraph with the same probability As we shall see in the proof of Theorem 1.2(b), if the degree sequence has bounded maximum degree then the underlying multigraph of a random ... minimum degree at least k, we define the low graph of H, L(H), to be the subgraph induced by the vertices of degree k In [16] Gallai characterized the set of graphs which are the low graphs of (k + 1)-critical...

Ngày tải lên: 07/08/2014, 06:20

... general lemma Lemma Assume that G is a negative dependency graph for the events A , A2 , , An Assume further that V (G) has a partition into classes, such that any two events in the same class have ... together with a family E(H) of subsets of V (H), which are called edges of H A r-uniform hypergraph, or r -graph, is a hypergraph whose edges have the same cardinality r The complete r -graph on ... = Pr (A1 |A2 ∧ A3 ∧ ∧ Ak ∧ Ak+1 ) Consider a set A with |A| = a and a set B with |B| = b, and assume a ≤ b Consider a random function f from A to B For u ∈ A, define the event Au = the value f...

Ngày tải lên: 07/08/2014, 15:23

... arguments can be adapted in order to characterize the distribution of the largest size of planar subgraphs of randomly chosen r–regular bipartite multi–graphs (Theorem 9) the electronic journal of combinatorics ... Even the constraint imposed by (iii) of Lemma 14 is standard (see again [BF02]) In the special case that r = 2, after re-scaling the x axis by a factor of 2, we get that the paths that satisfy ... In the next section we give a sketch and a proof of Theorem Both are straightforward adaptations of the proofs in [GWW98] dealing with the r = case In order to motivate the second main result of...

Ngày tải lên: 07/08/2014, 21:21

... which assumed no information in the essay Note that the actual dialogue depends on the correctness of the user answers After the dialogue, users were asked to revise their essay and then the system ... addition, the SIH is not always available and users have to activate it manually Other visual improvements for dialogue-based computer tutors have been explored in the past (e.g talking heads (Graesser ... Note that Figure is not a screenshot of the actual system interface The NM is the only part from the actual system interface Figure shows the NM after turn Tutor1 We manually annotated each system...

Ngày tải lên: 20/02/2014, 12:20

... concentrations were approximately doubled (194 lm p38 MAPKa, 549 lm ADP, 542 lm AMP-PCP) ATPase activity assay The ATPase activity of activated p38 MAPKa was characterized using the coupled assay ... obtained from the bisubstrate kinetics v A   ¼ Vmax aKA þ KB þ IKB þ I þ A 1 þ aKB Á B KI B B bKI rearranged v B     ¼ Vmax aKB þ KA þ IKA þ B þ aKA þ aKA I A KI A A bKI A ð2Þ MgADP We then ... recent years p38 MAPKa has emerged as a major practicable drug target, associated with several severe diseases of inflammation [3–5] The identification in 1994 of the pyridinyl class of p38 MAPKa inhibitors...

Ngày tải lên: 16/03/2014, 22:20

... perpendicular external magnetic field, both for the case of a single potential kink, as well as for a kink-antikink pair One advantage of such a setup is the fact that in an experimental realization of ... to the states that are indicated by arrows in panel (a) (a) (b) Figure Energy levels of a single kink profile in bilayer graphene as function of external magnetic field B0 with the same parameters ... coupling of the states localized at either potential interface Therefore, such configurable kink potentials in bilayer graphene permits the tailoring of the low-dimensional carrier dynamics as well as...

Ngày tải lên: 21/06/2014, 02:20

... algorithmic and can be used to construct a 3-colouring of any given petal graph, other than P ∗ We have indeed written a computer program, using Mathematica, which accepts as an input a petal graph G ... such that ∆(G∆ ) ≤ and ∆(G) = Let G = P ∗ Then G is Class The notion of petal graph will be particularly useful because, as we shall see, the proof of Theorem will be reduced to the proof of the ... petal graph with p = and n ≤ 9, the statement of the theorem holds trivially for n ≤ Assume now that n > 9, and that the statement of the theorem holds for any petal graph with order less than n...

Ngày tải lên: 07/08/2014, 07:21

... functions and the Tutte polynomial Preprint [10] Stanley, R P.: Hyperplane arrangements, parking functions and tree inversions In: Sagan, B and Stanley, R (eds) Mathematical Essays in Honor of Gian-Carlo ... that the vertices of Kn are labelled 1, 2, , n For a spanning tree A of Kn , an inversion in A is a pair of vertices labelled i,j such that i > j and i is on the unique path from to j in A ... is an increasing tree where all the vertices have at most edges going out A remarkable result stated in [4] and proved in [5] (see also a bijective proof in [3]) is that an equals the number of...

Ngày tải lên: 07/08/2014, 15:22

... Computing the orientable genus of projective graphs Journal of Graph Theory 20 (1995), 297–308 [8] M Juvan, A Malniˇ, and B Mohar Systems of curves on surfaces, Journal of c Combinatorial Theory ... and so in this case the number of crossings in D is within a constant factor ∆2 /(8cg ) of crg (G) Remark 4.2 In the planar case of Theorem 1.2, the described approximation algorithm yields a ... edges of C ∗ Then G − F is actually a plane embedding, and we easily add the edges of F back to G − F , making a plane drawing D with at most |F | pairwise crossings This whole algorithm can run...

Ngày tải lên: 07/08/2014, 15:23

... that of ‘addable’ edges: Definition Given a planar graph G, we call a non-edge e addable in G if the graph G + e obtained by adding e as an edge is still planar We let add(G) denote the set of addable ... H and each of these can have at most one ‘orientation’ that provides an appearance of H) Thus, when we deliberately constructed our appearance of H we can have only created at most |H| appearances ... enumeration and limit laws of planar graphs, Joure nal of the American Mathematical Society 22 (2009), 309–329 [6] S Janson, T Luczak, A Ruci´ ski, Random Graphs, Wiley (2000) n [7] C McDiarmid, A...

Ngày tải lên: 08/08/2014, 11:20

... this point The referee further remarked that the Flag graph of GH(2,2) can also be realized as the line graph of Tutte’s 12-Cage, or Benson’s graph In this table, we are employing the names given ... number of steps necessary for the random walk to travel from u to v and back to v, and in the case of distance regular graphs is equal to 2Hu v By Theorem in [5], the expected commute time of a random ... (2000) Distance-Regular Graphs of Valency and a1 = 1, Journal of Algebraic Combinatorics, v.11 n.2, p.101-134 [10] Jafarizadeh, M A. , Sufiani, R., Jafarizadeh, S (2009) Recursive calculation of effective...

Ngày tải lên: 08/08/2014, 12:22

... number of graphs in the sequence can be obtained by attaching ears serially or by bar-amalgamation of a cactus to GN Proof Suppose the values of the average genus of the graphs approach a finite ... is the frame of a cactus-free graph G F (G) Figure 2: A graph G and it’s frame Figure gives an example of a graph G and its frame F (G) In other words, a CF -graph can also be defined as a graph ... subgraph of Gi+1 for all i In [4] it was proved that the values of the average genus for 2-connected graphs have limit points Note that the average genus for bar-amalgamation of a cactus and the graph...

Ngày tải lên: 08/08/2014, 12:23

... for all graphs Next, we show that the lower bound to the tau constant of a banana graph Γ is ℓ(Γ) 16 For a banana graph Γ, a participant in the REU at UGA, Crystal Gordon, found by applying Lagrange ... dual graph of the special fiber of an algebraic curve C Similarly, Zhang [15] worked with an “admissible measure” µad , a generalization of µcan , of total mass on Γ The diagonal values gµcan (x, ... and J Laurie Snell, Random Walks and Electrical Networks, Carus Mathematical Monographs, Mathematical Association of America, Washington D.C., 1984 [10] X W.C Faber, Spectral convergence of the...

Ngày tải lên: 08/08/2014, 14:23

... in determining the mutation class of a quiver In [2], the authors prove that the mutation class of an adjacency matrix associated to a triangulation of a bordered surface with marked points is ... decomposable, we may break connectivity of a graph in only two trivial cases In either case, the resulting graph contains isolated nodes On the other hand, in a decomposable graph, isolated nodes can ... graph has a unique decomposition, so does the original graph the electronic journal of combinatorics 18 (2011), #P91 43 As an application of the algorithm we can classify all decomposable graphs...

Ngày tải lên: 08/08/2014, 14:23

... The line graph, LG, for G is the multidigraph whose vertices are the edges of G and whose edges are (e, f ) with e+ = f − As with G, we have the Laplacian ∆LG and the critical group ... [1] Andrew Berget, Andrew Manion, Molly Maxwell, Aaron Potechin, and Victor Reiner The critical group of a line graph arxiv:math.CO/0904.1246 [2] Alexander E Holroyd, Lionel Levine, Karola M´sz´ros, ... Theorem and may be seen as analogous to Theorem 1.2 of [3] In [3], partially for convenience, some assumptions are made about the connectivity of G which are not made in this note For related work...

Ngày tải lên: 08/08/2014, 14:23