Báo cáo toán học: "Component evolution in random intersection graphs" ppsx

... Component evolution in random intersection graphs Michael Behrisch ∗ Institut f¨ur Informatik, Humboldt-Universit¨at zu Berlin, 10099 Berlin, Germany behrisch@informatik.hu-berlin.de Submitted: ... Colouring random intersection graphs and complex networks. Preprint, December 2005. [4] B. Bollob´as and O. Riordan. Slow emergence of the giant component in the growing m-out graph....

Ngày tải lên: 07/08/2014, 15:22

... cycles in random regular graphs, J. Combin. Theory, Ser. B 31 (1981) 168–182. [11] N. C. Wormald, Models of random regular graphs. In J.D. Lamb and D.A. Preece (eds.), Surveys in Combinatorics ... argument, since the special case we will need is one where the lemma is vacuously true. Lemma 2 A random G in R(m 1 , ,m t ) has at most Q edges contained in cycles whose length is...

Ngày tải lên: 07/08/2014, 08:20

... strings corresponding to some standard Young tableau of shape λ beginning with some string w of length i − 1 followed by a, b and c in some order and ending by some v. We may neglect the strings ... tableau also corresponds to a string of numbers formed by reading the numbering in the order determined by the tableau. (This has been called the inverse reading word of the tableau.) A standa...

Ngày tải lên: 07/08/2014, 06:22

... vertices in graphs, IEEE Transactions on Information Theory, vol 44, pp. 599-611, 1998. [6] A. Lobstein, Bibliography on identifying and locating-dominating codes in graphs, http://www.infres.enst.fr/∼lobstein/debutBIBidetlocdom.pdf [7] ... minimal r-twin-free graph for the induced subgraph relationship. Indeed, we have: the electronic journal of combinatorics 15 (2008), #N17 5 An r-twin-...

Ngày tải lên: 07/08/2014, 15:22

... Theorem 1.2 and it serves as an introduction to it. We begin with a lemma about selecting induced forests of a particular kind in a bipartite graph. We introduce some terminology. Let H be a bipartite ... ··· ∪ M  induces a forest in G. We let T be the component of this forest containing the single vertex of M  . Since every vertex of M i−1 ,  < i ≤ k, has at least one neighbor in...

Ngày tải lên: 07/08/2014, 15:23

... set of |T | distinct colors on some such set of |T | edges between S and distinct vertices of T . In [15], we obtained the following result concerning heterochromatic matchings in colored bipartite ... partitioned into sets V 1 , · · · , V r in such a way that each hyperedge meets each V i in precisely one vertex. A matching in a hypergraph is a set of disjoint hyperedges. The match...

Ngày tải lên: 07/08/2014, 21:21

... edges joining u j to U have color λ 2 , and all edges joining v j to V have color λ 1 . If U and V are both nonempty, then replacing u j v j with edges to each yields a larger rainbow matching in ... for K 4 or a graph obtained from K k+2 by removing a matching. A survey on rainbow matchings and other rainbow subgraphs appears in [1]. Subgraphs whose edges have distinct colors have also b...

Ngày tải lên: 08/08/2014, 11:20

... is minimal, since every cycle has length 3. But it is non-fundamental, since every edge is covered at least two times. The concept of fundamental has originally been introduced by Kirchhoff in ... (B)=  C∈B |C|.Aminimal cycle basis is a cycle basis with minimal length. Let c(B) be the length of the longest cycle in the cycle basis B. Chickering [3] showed that if (B) is minimal then c(B...

Ngày tải lên: 07/08/2014, 06:22

... denotes the set of neighbors of z. Counting the edges between S i and L i+1 as seen from L i+1 (again counting twice those in the intersection) , we obtain s i ((i − 1)l i+1 + im) ≤ is i |Z| +  (i ... not contain F as a subgraph. Then G contains a set E  of less than cn 2 edges such that the subgraph G  obtained from G by deleting all edges in E  has no K r+1 . the electronic journal...

Ngày tải lên: 07/08/2014, 13:21

... intersection of the corresponding circles of radius ρ would contain all the neighbors, but this intersection is contained in a circle of smaller radius. Lemma 1 (No local minimum besides global one). ... jammed embedding then let us denote by G O the pseudo–embedding obtained from G by adding the edges of C O ; let us note that C O bounds the outer face of G O . In a jammed embedding...

Ngày tải lên: 07/08/2014, 13:21