4 adjust the maximum number of parallel execution processes
Báo cáo toán học: "The maximum number of perfect matchings in graphs with a given degree sequence" docx
Ngày tải lên :
07/08/2014, 15:22
... permutation of rows and columns A is a block diagonal matrix in which each block is a square all-1 matrix Proof of Theorem 1.1: The square of the number of perfect matchings of G counts ordered pairs of ... contribution to the permanent) Thus the square of the number of perfect matchings is at most the permanent of the adjacency matrix, and the desired inequality follows from Bregman-Minc by taking the square ... every cycle of length exceeding in H there are two ways to decide which edges came from M1 and which from M2 The permanent of the adjacency matrix A of G also counts the number of spanning 2-regular...
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Tài liệu Báo cáo khoa học: "Selecting the “Right” Number of Senses Based on Clustering Criterion Functions" pdf
Ngày tải lên :
22/02/2014, 02:20
... total of 88 experiments The results are shown in Tables 1, 2, and In these tables, the actual numbers of senses are in the columns, and the predicted number of senses are in the rows We see that the ... introduces the L measure This tries to find the point of maximum curvature in the criterion function graph, by fitting a pair of lines to the curve (where the intersection of these lines represents the ... single threshold The graph of the P K1 scores shown in Figure illustrates the difficulty - the slope of these scores is nearly linear, and as such the threshold (as shown by the horizontal line)...
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Đề tài " The two possible values of the chromatic number of a random graph " pot
Ngày tải lên :
29/03/2014, 07:20
... convexity, Jk is the maximizer of the entropy over Bk and the minimizer of the 2-norm By the same token, the permutation matrices are minimizers of the entropy and maximizers of the 2-norm The constant ... Specifically, the number of k-colorings of a random graph is the sum, over all k-partitions σ of its vertices (into k “color classes”), of the indicator that σ is a valid coloring To estimate the second ... progress was made on the problem Specifically, by the mid 1970s, the expected value of χ(G(n, p)) was known up to a factor of two for the case of fixed p, due to the work of Bollob´s and Erd˝s...
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Báo cáo hóa học: " On the maximum modulus of a polynomial and its polar derivative" potx
Ngày tải lên :
20/06/2014, 22:20
... kn Proof of the theorem Proof of Theorem 1.1 Let m = min|z|=k |p(z)| If p(z) has a zero on |z| = k, then m = and the result follows from Lemma 2.8 Henceforth, we suppose that all the zeros of p(z) ... contradicts the fact that |a1| >k Hence, the polynomial Dα1 p(z) must be of degree (n - 1) On the other hand, since all the zeros of p(z) lie in |z| ≤ k, therefore by applying Lemma 2.1, all the zeros of ... denote the polar differentiation of the polynomial p(z) of degree n with respect to a Î ℂ Then, Dap(z) = np(z) + (a - z)p’(z) The polynomial Da p(z) is of degree at most n - 1, and it generalizes the...
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Báo cáo toán học: "The independence number of graphs with large odd girth" ppt
Ngày tải lên :
07/08/2014, 06:20
... still find bounds for the independence number in terms of the odd girth, but instead of the average degree of the graph we have to use another measure of the concentration of edges ... independent set of the other size we mimic the proof of Theorem but this time we choose k n m= k∆0 Let us colour the vertices of G with (k − 1)m colours Clearly if any sm colour classes together contain ... be the number of pairs of adjacent vertices of degree in G Let f (0) = 1, f (1) = 4/7 and f (d) = [1 + (d2 − d)f (d − 1)](d2 + 1)−1 when d ≥ Then n α(G) ≥ f(di ) − n11 /7 i=1 The results of...
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Báo cáo toán học: "THE INDEPENDENCE NUMBER OF DENSE GRAPHS WITH LARGE ODD GIRTH" ppsx
Ngày tải lên :
07/08/2014, 06:20
... We can now prove the following theorem ¯ Theorem Suppose G contains no or cycles Let d be the average degree of vertices of G Then ¯ α(G) ≥ nd/2 Proof Since G contains no or cycles, ... (k ≥ 2) Then α(G) ≥ 2−( k−1 k ) n k−1 d k k Proof Immediate from Theorem This improves Denley’s Theorem References Denley, T., The Independence number of graphs with large odd girth, The Electronic ... 2) Then v∈G + d1 (v) + · · · + dk−1 (v)) + d1 (v) + · · · + dk (v) (1 α(G) ≥ v∈G Proof Randomly label the vertices of G with a permutation of the integers from to n Let A (respectively B) be the...
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Báo cáo toán học: "The asymptotic number of set partitions with unequal block sizes" pot
Ngày tải lên :
07/08/2014, 06:20
... immediately from the fact that in the proof of Theorem 2.1 for the case k = m − s, the di represent the holes in the partition Proofs of lemmas Proof of Lemma 3.1 If r ≥ m + 1, then r i=1 hi ≥ ... Proof of Theorem 2.3 The last part of the theorem, referring to m − k bounded, is the same as in Theorem 2.1 For m − k → ∞ but k = o(m), the theorem is covered by Proposition 2.1 together with the ... measure of the behavior of bn is that it compares bn to the contribution of the largest term, which does not behave smoothly Table presents another measure of the irregularity in the behavior of the...
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Báo cáo toán học: "An improved bound on the minimal number of edges in color-critical graphs" pot
Ngày tải lên :
07/08/2014, 06:22
... ingredient of our proof is the following result of Stiebitz Lemma ([5]) Let G be a k-critical graph containing at least one vertex of degree k − Then the number of connected components of its high-vertex ... H(G) does not exceed the number of connected components of its low-vertex subgraph L(G) Proof of Theorem Let L(G) and H(G) be the low-vertex and the high-vertex subgraphs of G, respectively Denote ... (we follow the terminology of [4]) If G = (V, E) is a k-critical graph, then the low-vertex subgraph of G, denoted by L(G), is the subgraph of G, induced by all vertices of degree k − The high-vertex...
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Báo cáo toán học: "On the Domination Number of a Random Graph" docx
Ngày tải lên :
07/08/2014, 06:22
... concentration for the domination number Dn of the subgraph G(n, p) of G( +, p), p fixed Specifically, we shall prove Theorem Consider the infinite random graph G( +, p), where p is fixed Let È be the measure ... Concentration For r ≥ 1, let the random variable Xr denote the number of dominating sets of size r Note that (n ) r Xr = Ij , j=1 where Ij equals one or zero according as the j th set of size r forms or ... moreover, that the argument leading to (3) is otherwise independent of the magnitude of p (since (log n)Ä ((Ä n)(log n)) always far exceeds 2Ä n), so that we have Lemma The conclusion of Lemma holds...
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Báo cáo toán học: "The minimum number of monotone subsequences" pptx
Ngày tải lên :
07/08/2014, 07:21
... order the k subsequences by the position of their middle element (the leftmost of two middle elements, if the sequence is k of even length) There are n mod k choices of the i satisfying these ... sj + k − } Put S = ∪k Sj Then S is the union of j=0 the sets of the k − values (or positions) at either end of each of the subsequences in the canonical extremum Write the canonical extremum as ... Now, the values of ci for i ∈ S0 are the values of R0 in descending order; the values of ci for i ∈ Sk are the values of Lk in descending order; the values of ci for i ∈ Bj are the values of Lj...
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Báo cáo toán học: "On the crossing number of Km,n" potx
Ngày tải lên :
07/08/2014, 07:21
... is defined in the same way as in the proof of Lemma Lemma Let λ be the number of distinct pairs of elements of B having the same cyclic ordering of edges incident on an element of A Then, if n ... and the elements of B are b1 , b2 , , bn In a drawing D, we denote by crD (ai , ak ) the number of crossings of arcs, one terminating at , the other at ak and by crD (ai ) the number of crossings ... elements of T are t0 , t1 , Let η be the number of pairs {tk ∈ T, tk ∈ T } such that crD5,z (tk , tk ) ≥ ≥ Z(3, 5) + Then Z(5, z) + 2η ≤ crD5,z Proof:Let h(tk ) be the sum of the number of crossings...
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Báo cáo toán học: " On the chromatic number of intersection graphs of convex sets in the plane" ppt
Ngày tải lên :
07/08/2014, 08:20
... 4)-degenerate The idea of the proof of Theorem allows us to estimate the maximum degree of the intersection graph Theorem Let G be the intersection graph of translations of a fixed compact convex set in the ... intersects V Case yu < yv Repeating the proof of Case with roles of A and B switched yields this case The proof of Claim 3.2 is the same (with C in place of B) Proof of Claim 3.3 Let A∗ = 2A, B ∗ = ... , the same lemma yields that v + A intersects u + A This proves the claim and thus the theorem Clearly, Theorem implies Theorem Now we also derive Theorem Proof of Theorem Let A be a member of...
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Báo cáo toán học: "The spectral radius and the maximum degree of irregular graphs" doc
Ngày tải lên :
07/08/2014, 15:22
... similar to the one of the previous case, we can easily finish the proof of the theorem We claim there exists j ∼ s such that xj < √n Otherwise, let j ∼ s such that d(j, w) = D − Then applying the argument ... necessarily regular) graph G and that of a subgraph of G, see [16] The spectral radius and the maximum degree The following theorem is the main result of this section Theorem 2.1 Let G be a connected ... bounds for the distance between vertices corresponding to the extreme entries of the principal eigenvector of an irregular graph G, then one can improve the result of Theorem 2.1 However, there are...
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Báo cáo toán học: "The crossing number of a projective graph is quadratic in the face–width" doc
Ngày tải lên :
07/08/2014, 15:23
... from V (G) The faces of G traversed by γ then define in this order the vertex set of a noncontractible dual cycle C ∗ , and so ≤ |V (C ∗ )| ≤ r∆/2 Proof of Theorem 1.2 The idea of the previous ... This gives the following special (planar) version of Theorem 1.1 Theorem 3.4 If G embeds in the projective plane with face–width at least r ≥ 6, then the crossing number crg (G) of G in the plane ... in the projective plane with face–width r Then the crossing number of G in the plane (and thus in any orientable surface) is at most r ∆2 /8 Proof Consider , the dual edge-width of G—i.e the...
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Báo cáo toán học: "On the chromatic number of simple triangle-free triple systems" pps
Ngày tải lên :
07/08/2014, 21:20
... chromatic number, although we phrase it only for chromatic number In the next section we present the lower bound in Theorem and the rest of the paper is devoted to the proof of the upper bound The ... be the vertex set of H As usual, we write χ(H) for the chromatic number of H Let ε > be a sufficiently small fixed number Throughout the paper, we will omit the use of floor and ceiling symbols the ... multiplicative factor of (1 − 1/ log ∆), and so the number of steps in the semi random phase of the algorithm is roughly log ∆ log log ∆ In principle our method is the same, but there are several...
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Báo cáo toán học: "The Ramsey number of diamond-matchings and loose cycles in hypergraphs" potx
Ngày tải lên :
07/08/2014, 21:20
... proof In fact, the proof method of Theorem can be copied to determine the 3-colored Ramsey number of the diamond-matching as well Theorem For every k ≥ 1, r ≥ 2, R(kDr , kDr , kDr ) = 2kr − Proof ... and prove the Ramsey-type form of our main result, it determines the exact value of the Ramsey number of a diamond-matching the electronic journal of combinatorics 15 (2008), #R126 Theorem For ... reduces the problem of finding the Ramsey number of a path or a cycle to finding the Ramsey number of a connected matching An additional - usually technical - difficulty is that the coloring is not on the...
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Báo cáo toán học: "The maximum size of a partial spread in H(4n + 1, q 2) is q 2n+1 + 1" docx
Ngày tải lên :
07/08/2014, 21:21
... all of them eigenspaces of the relations Rj of the association scheme The (D + 1) × (D + 1)-matrix P , where Pij is the eigenvalue of the relation Rj for the eigenspace Vi , is the matrix of eigenvalues ... eigenvalues of the association scheme If ∆m is the diagonal matrix with (∆m )ii the dimension of the eigenspace Vi , and if ∆n is the diagonal matrix with (∆n )jj the valency of the relation Rj , then the ... ci are known as the intersection numbers of the distance-regular graph Γ If θ is any eigenvalue of a distance-regular graph Γ, then there is a series of eigenvalues {vi } of the associated i-distance...
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Báo cáo toán học: "Sharp lower bound for the total number of matchings of tricyclic graphs" doc
Ngày tải lên :
08/08/2014, 12:22
... with the framework of the HMO approximation [18, 19], the theory of graphic spectra and nullity of graphs; see [3, 9, 10, 11, 17]), whereas to our best knowledge, the total number of matchings of ... index of hexagonal spiders In light of the information available for the total number of matchings of trees, unicyclic graphs, bicyclic graphs, it is natural to consider other classes of graphs, ... on the total number of matchings of tricyclic graphs with n vertices? Acknowledgments The authors would like to express their sincere gratitude to the referee for a very careful reading of the...
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Báo cáo toán học: "A new bound on the domination number of graphs with minimum degree two" docx
Ngày tải lên :
08/08/2014, 12:23
... detailed proof of Theorem is very technical, we provide here only a summary of the main ideas of the proof A detailed proof of Theorem is provided in the appendix the electronic journal of combinatorics ... v in the unit and we call these three vertices the attachers of the cycle-unit, while in a key-unit we call the vertex of degree one the attacher of the key-unit Let G denote the family of all ... any number of link edges, including the possibility of zero Every edge of G joining two attachers we call a link edge of G and we call the resulting two attachers link vertices of G A graph in the...
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