Báo cáo toán học: "Short cycles in random regular graphs" pps

... short 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 ... questions, the most “interesting” subgraphs are the cycles. For this reason we consider only cycles in this paper. The girth of the graph is an interesting property which...

Ngày tải lên: 07/08/2014, 08:20

... 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. to app...

Ngày tải lên: 07/08/2014, 15:22

... deg + (u)+deg + (v) ≥ 3 for all pairs of distinct vertices u, v in G,theng ≤n/2. 2 Main Results Suppose u is a vertex in G. If a digraph G  is obtained from G by adding to it an extra vertex u  and ... n/2. Applying the above- mentioned result, we improve their result by replacing the minimum outdegree con- dition by some weaker conditions involving the local average outdegree. In...

Ngày tải lên: 07/08/2014, 07:21

... correspondance. In this paper we are going to investigate another natural question of this type (also initiated by the first author), namely what can we say about cycles in G(A). Thecaseof even cycles ... from the following theorem in [9]: If n ≥ n 0 , |A (2,1) | = s>0, |A| >f(n, 1) and r =min{s,  1 10 log log n},thenK(r, r) ⊂ G(A). The case of odd cycles is more interestin...

Ngày tải lên: 07/08/2014, 06:22

... vertices in this figure are arranged in three concentric rings, each inducing one of the six consistent 9- cycles in the orbit. These three consistent cycles share the same shunt, being the rotation of ... going between the rings induce the other three consistent cycles in the orbit. Now consider the drawing of the Doyle-Holt graph in Figure 2. Here the vertices are arranged i...

Ngày tải lên: 07/08/2014, 21:21

... 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