Báo cáo toán học: "Loose Hamilton Cycles in Random 3-Uniform Hypergraphs" doc

... terminology. Let H be a random variable which counts the number of loose Hamilton cycles in Λ d such that the edges only intersect in X. Note that every such loose Hamilton cycle induces an ordinary ... Hamilton cycles in random 3-uniform hypergraphs, Electronic Jour- nal of Combinatorics 17 (2010), N28. [5] A.M. Frieze, M. Jerrum, M. Molloy, R. Robinson and N. Wormald,...

Ngày tải lên: 08/08/2014, 12:23

... contiguity, Combi- natorics Probability and Computing 4 (19 95) 369-405. [5] S. Janson and N. Wormald, Rainbow Hamilton cycles in random regular graphs, Random Structures Algorithms 30 (2007) 35-49. [6] ... If G ∗ contains a rainbow Hamilton cycle, then H contains a loose Hamilton cycle. We will use Theorem 2 to show that whp G ∗ contains an edge coloured graph that is close to...

Ngày tải lên: 08/08/2014, 11:20

... Hamiltonian cycles in random graphs. Annals of Discrete Mathematics 28 (1985) 23-46. [6] B. Bollob´as, T.I. Fenner and A.M. Frieze. An algorithm for finding Hamilton cycles in random graphs. Combinatorica ... Frieze. Hamilton cycles in random graphs with minimal degree at least k. (A Tribute to Paul Erd˝os (A.Baker, B.Bollobas and A.Hajnal; Ed)) (1990) 59-96. [8] C. Coope...

Ngày tải lên: 07/08/2014, 06:20

... 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 joining ... edge going from this 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...

Ngày tải lên: 07/08/2014, 07:21

... endpoints x, y. As C is closed, every point in P \ C is contained in a C-arc in P. Suppose no C-arc in P is a shortcut of C. We can find a family (W i ) i∈N of countably many internally disjoint ... disjoint arcs in P , such that fo r every i, W i is either a C-arc or an arc cont ained in C, and every edge in P lies in some W i (there may, however, exist ends in P that are no...

Ngày tải lên: 08/08/2014, 01:20

... not all distinct. Thus a set S of vertices of Γ is independent if and only the set of edges obtained by taking, each e = {e 0 ,e 1 }∈S and replacing it by (e 0 ,e 1 ), (e 1 ,e 0 ) (giving 2|S| directed ... Theorem 4 to obtain a slight strengthening of Theorem 1 viz. there is a Hamilton cycle and its reversal spanning a multicoloured set of directed edges. the electronic journal of combinato...

Ngày tải lên: 07/08/2014, 06:20

... 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 in which every ideal ... of combinatorics 12 (2005), #R52 10 A Dedekind ring is simply a quotient of a Dedekind domain. If R is a Dedekind domain, and m i is a maximal ideal of R,thenR/m i is a field and thus cont...

Ngày tải lên: 07/08/2014, 13:21

... 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 journal of combinatorics ... fixed points of L in our underlying Euclidean space and then monotonicity leads us to the rest. Fixed “points” will no longer remain the key in the general argument but as w...

Ngày tải lên: 07/08/2014, 15:23

... family of all minimum dominating sets of Γ(Z n 2n+1 , U). Note that since Γ(Z n 2n+1 , U) is regular and contains at least one perfect dominating set, a set S ⊆ V (G) is a minimum dominating set if ... perfect dominating sets with defining number 2 (See Remark 3). So far there is no nontrivial bound known for the defining numbers of minimum dominating sets of Γ(Z n 2n+1 , U). We prove the follo...

Ngày tải lên: 07/08/2014, 13:21

... the coordinates in I this slice projects onto the gra ph C d−|I| 2n+1 . Furthermore, if S is an independent set in C d 2n+1 then S intersected with the slice maps onto an indep endent set in C d−|I| 2n+1 under ... determine the location of the one vertex in S ∩ K v by parity.) Also note that the holes in a slice of an independent set S correspond to holes in H(S). We say that inde...

Ngày tải lên: 07/08/2014, 21:21