Báo cáo toán học: "he spectral gap of random graphs with given expected degrees" pot

... exp(− ¯ d min /(2C)), the electronic journal of combinatorics 16 (2009), #R138 44 The spectral gap of random graphs with given expected degrees ∗ Amin Coja-Oghlan University of Edinburgh, School of Informatics Crichton ... graphs with with given degree sequences. Random Structures and Algorithms 32 (2008) 1–19 [7] Chung, F., Lu, L.: Connected components in rando...

Ngày tải lên: 08/08/2014, 01:20

... of G. If H is a component of G − e with µ (H) = µ (G − e) , then µ (G) − µ (H) > 1 Diam (H) |H| . This lemma follows easily from Theorem 2.1 of [2] and its proof is omitted. Proofs Proof of ... the proof. ✷ Proof of Theorem 3 Let x = (x 1 , . . . , x n ) be an eigenvector to µ min (G) and let U = {u : x u < 0} . Write H for the bipartite subgraph of G containing all edges...

Ngày tải lên: 07/08/2014, 13:21

... d k−1 (v)) 1+d 1 (v)+···+ d k (v) . Proof. Randomly label the vertices of G with a permutation of the integers from 1 to n.LetA (respectively B) be the set of vertices v of G such that the minimum label ... 2 − ( k−1 k ) n k−1 k d 1 k . Proof. Immediate from Theorem 3. This improves Denley’s Theorem 4. References 1. Denley, T., The Independence number of graphs with large odd...

Ngày tải lên: 07/08/2014, 06:20

... values of n, we shall use elementary estimates and some well-known bounds for ordinary partitions (of a number) to express most values of b n in terms of the number of ordinary partitions of k with ... the number of partitions of (the number) n,andQis its ordinary generating function. Also, define p(n, k) to be the number of partitions of n with largest part at most k. W...

Ngày tải lên: 07/08/2014, 06:20

... between A and B. Proof The proof follows that of Lemma 5. By P6, the number of edges between A and B in G of a colour different to that of any edge incident with a vertex of SMALL is at least M ... a growing literature on the subject of the Ramsey properties of random graphs, see for example the paper of R¨odl and Ruci´nski [17]. 2 Outline of the proof of Theorem 1 We...

Ngày tải lên: 07/08/2014, 06:20

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Ngày tải lên: 05/08/2014, 15:21

... isomorphism of Proposition 5.1 we transfer our probability distribution to the set of m–tuples of Young disgrams with total number of boxes equal to n. Then by (5.2) we see that the probability of an ... correspondence with pairs of 2–rim hook tableaux of the same shape with 2n boxes and width l. The length of the longest increasing subsequence for signed permutations em...

Ngày tải lên: 07/08/2014, 06:20

... (V C ,C)ofG(V,E). The set C of all cycles forms a subspace of (E, ⊕, ·) which is called the cycle space of G.AbasisBof the cycle space C is called a cycle basis of G(V, E) [2]. The dimension of the ... number of its edges. The length (B) of a cycle basis B is sum of the lengths of its cycles: (B)=  C∈B |C|.Aminimal cycle basis is a cycle basis with minimal length. Let c...

Ngày tải lên: 07/08/2014, 06:22