Báo cáo toán học: "Bent Hamilton Cycles in d-Dimensional Grid Graphs" pdf

... the dimension of joining. Then P must contain w disjoint bent cycles that partition the vertices of P . Each of these w cycles must contain a wrapped edge in P along the joining dimension. Further, ... 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 repeated...

Ngày tải lên: 07/08/2014, 07:21

... 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

... 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

... 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

... 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

... the beginning of w. 4 Words containing in nitely many overlaps In this section we construct various in nite α power-free binary words containing in nitely many overlaps. We begin by considering ... 68R15 Abstract We characterize the squares occurring in infinite overlap-free binary words and construct various α power-free binary words containing in nitely many overlaps. 1 Introduction...

Ngày tải lên: 07/08/2014, 13:21