Báo cáo toán học: "Geodetic topological cycles in locally finite graphs" docx

... K¨uhn. On in nite cycles I. Combinatorica, 24:68–89, 2004. [11] R. Diestel and D. K¨uhn. On in nite cycles II. Combinatorica, 24:91–116, 2004. [12] R. Diestel and D. K¨uhn. Topological paths, cycles ... cycle space of locally finite in nite graphs. The topological cycle space C(G) of a locally finite gra ph G was introduced by Diestel and K¨uhn [10, 11]. It is built not...

Ngày tải lên: 08/08/2014, 01:20

... endpoint in S, the other a distinct endpoint not in S and of a colour different to that of any edge incident with a vertex of SMALL. This set of edges contains at least |M|/k colours. If M contains ... combinatorics 2 (1995), #R19 6 5 Binomial tails We make use of the following estimates of tails of the Binomial distribution several times in subse- quent proofs. Let X be a random variabl...

Ngày tải lên: 07/08/2014, 06:20

... endpoint to the corresponding endpoint in level i − 1. Similarly, if an endpoint in level i has no surrounding circle then there is an edge going from such an endpoint to a corresponding endpoint ... we join the endpoints with red arrows pointing away from each other to create the new wrapped edges in G + P . We thus obtain a bent Hamilton cycle in Q  (5, 3, 3), and by repeatedly joi...

Ngày tải lên: 07/08/2014, 07:21

... graphs. In partic- ular, it allows us to generalize to unitary circulant graphs on Dedekind rings. Definition 4.6. A Dedekind domain ([3]) is an integral domain R such that (1) Every ideal in R is finitely ... maximum lengh of a cycle in unit circulant graphs on a Dedekind domain quotiented by an ideal with r distinct maximal factors. Dedekind domains are exactly those integral domains i...

Ngày tải lên: 07/08/2014, 13:21

... (1) Theorem 4 is proved in Janson [4] (Theorem 11) and in Molloy, Robalewska-Szalat, Robin- son and Wormald [8]. 2 Proof of Theorem 1 We begin by letting Y be a set of size 2 rm consisting of r = O(1) ... Y j , p 1 ) contains a perfect matching M j . (We need the split into r copies of H n,p 2 ;3 to allow a “colour” to appear several times in a matching). Now each perfect matching M j g...

Ngày tải lên: 08/08/2014, 11:20

... partitioned into 2m cells X x , x ∈ X of d points. Analogously Y is represented as dκm points partitioned into 2κm cells Y y , y ∈ Y of d/2 points. To construct Λ d we take a random pairing of X into ... ways of defining Hamilton cycles in hypergraphs, depending on the size of the intersection of successive edges. As far as we know, when these intersections have more than one vertex, nothi...

Ngày tải lên: 08/08/2014, 12:23

... having at most 100 points. 9 Concluding remarks. 9.1. Classical Seidel’s switching is certainly the first origin of this paper. It goes back to the paper [vLinS66]. Explicitly the notion was introduced ... purpose we were using the following functions from COCO: ind, cgr, inm, sub,andaut. We describe below each of these functions. • ind input1.gen input2 output1.gen output2.map Starting from p...

Ngày tải lên: 07/08/2014, 07:21

... Tuza, Rainbow Hamiltonian paths and canonically colored sub- graphs in infinite complete graphs, Mathematica Pannonica 1 (1990), 5–13. [7] P. Erd˝os and Zs. Tuza, Rainbow subgraphs in edge-colorings ... vertices are joined by an edge if and only if they differ in exactly one coordinate or they differ in all coordinates. An edge is in color j (1 ≤ j ≤ k − 1) if and only if its two ends...

Ngày tải lên: 07/08/2014, 13:21

... symmetric sequences. Before beginning in earnest, let us mention the main steps. By looking at the leading order behavior we find hypersurfaces bounding the region of in nite logconcavity. We proceed ... hypersurfaces in turn and iterating. The technical key to controlling the iteration is understanding the effect of increasing one coordinate while decreasing all the others. the electronic...

Ngày tải lên: 07/08/2014, 15:23

... r unitarily invariant norms, in particular for the spectral and Hilbert-Schmidt norms [3]. Perturbations in the  ·  ∞ norm has been studied in the Markov Chain literature [14] to investigate ... B. Sudakov. Finding a large hidden clique in a random graph. In Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 594-598, 1998. [3] R. Bhatia. Matrix Analysis. Springer-Verla...

Ngày tải lên: 08/08/2014, 01:20