Báo cáo toán hoc:"Vertex-oriented Hamilton cycles in directed graphs" pot

... 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 ... 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. Cooper. 1-pancyclic Ham...

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

... 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 satisfying the conditions ... (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 consi...

Ngày tải lên: 08/08/2014, 11:20

... 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 ... 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 ve...

Ngày tải lên: 08/08/2014, 12:23

... 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

... 1-factor containing e,so does G ∗ . By Theorem 1, G ∗ has a k-factor containing e and another k-factor avoiding e for all k,1≤ k ≤ 2r − 1. Deleting the matching M from G ∗ ,weobtaina[k, k + 1]-factor the ... 1)-factor containing e and G − F 1 is an (r − 1)-factor avoiding e. By Theorem 2, the odd-factors F 1 and G − F 2 containing e, respectively, imply the existence of k-factors containing e...

Ngày tải lên: 07/08/2014, 08:22

... D. A directed Hamilton cycle H in D is a Hamilton cycle in the graph underlying D such that all pairs of consecutive arcs in H form a directed path in D. An anti -directed Hamilton cycle H in D is ... ideas of a directed Hamilton cycle and an an anti -directed Hamilton cycle, because a directed Hamilton cycle in D is a (∅, V (D)) vertex-oriented Hamilton cy...

Ngày tải lên: 08/08/2014, 01:20

... 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

... 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

... eects monitoring plays an important role in marine monitoring. Contaminants and their eects on sh as well as on other marine organisms belong to the main topics of international monitoring schemes. ... drawbacks of choosing and applying marker of contaminant eects to marine eld samples. It reects the actual stage of international guidelines for biological eects monitoring in mari...

Ngày tải lên: 20/06/2014, 20:20