Báo cáo toán học: "Partitions and Edge Colourings of Multigraphs" pps

... loops. The edge set and the vertex set of G is denoted by V (G) and E(G) respectively. For a vertex v of G, the degree, d(v), of v in G is the number of edges incident with v. The set N v of all ... the edges of G may be coloured so that no two adjacent edges receive the same colour. A triangle in G is a set of three mutually adjacent vertices in G, and the edges of a...

Ngày tải lên: 07/08/2014, 15:22

... d is odd and the edge set of G can be partitioned into the edge sets of (d − 3)/2 disjoint Hamilton cycles and one cubic graph then ndi(G) ≤ 3d/2. (ii) If d is even and the edge set of G can ... adjacent to edges coloured α, β and so is w, and all adjacent vertices of H 2 the electronic journal of combinatorics 13 (2006), #R77 7 Neighbour-distinguishing edge col...

Ngày tải lên: 07/08/2014, 13:21

... face of G  . We know that it is a subdivision of C 2 , and each edge of F belongs to one of the two sides of C 2 . Lemma 8. Let e be an edge of G  and let l be the line in the plane (cycle on ... G 1 and G 2 in the embedding of G. G 1 is completely embedded in one of the faces of G 2 and vice versa, which is not possible by convexity of faces and by Lemma 1...

Ngày tải lên: 07/08/2014, 13:21

... absorbers hav ing energy band gaps in the range of 1.3 to 1.5 eV compared with CdS and having a wider energy band gap compared with CdS, which trans- mits even higher energy photons and increases the ... National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0024830). Author details 1 School of Materials Science and Engine...

Ngày tải lên: 20/06/2014, 21:20

... study and participated in its design and coordination. CY participated in the revision of the manuscript. LPS and YW participated in the preparation of the TiO 2 /ZrO 2 bilayer thin film. JQZ and ... 7:31 http://www.nanoscalereslett.com/content/7/1/31 Page 3 of 5 Acknowledgements This work is supported in part by the National Nature Science Foundation of China (No. 51072049),...

Ngày tải lên: 20/06/2014, 21:20

... Semigroups Yupaporn Kemprasit 1 and Sawian Jaidee 2 1 Department of Mathematics, Faculty of Science Chulalongkorn University, Bangkok 10330, Thailand 2 Department of Mathematics, Faculty of Science , Khon ... set of integers and the set of real numbers, respectively. In [3], Kemprasit and Changphas characterized when OT (X) is regular where X is a nonempty subset of Z or X...

Ngày tải lên: 06/08/2014, 05:20

... those of the author(s) and do not necessarily reflect the views of the NSA. the electronic journal of combinatorics 11 (2004), #R4 1 2 The Proofs Let n(G) denote the number of vertices of a graph ... N(z) since d(x) ≥ d(z), and the 2-switch that replaces wz and xy with wx and zy reduces the number of missing desired neighbors of w. Theorem 4 For a positive list X and no...

Ngày tải lên: 07/08/2014, 08:20

... limit distribu- tions of the number of edges in a random dissection and in a random outerplanar graph, respectively. Proof of Theorem 1.4. The limit distribution of the number of edges in a two-connected unlabeled ... probability of connectedness, the number and type of components, and the number of isolated vertices, in a random outerplanar graph. Next, we investigate t...

Ngày tải lên: 07/08/2014, 15:23

... is equal to the number of sequences over {0, 1, 2, 3} of length n with n − l(α) occurrences of 0, m 1 (α) occurrences of 1, m 2 (α) occurrences of 2 and one occurrence of 3 (as specified by P 3 ). 12 (3) ... is known that [M] each of the sets {h λ }, {m λ } ,and{ p λ },whereλ ranges over all partitions of n, is a basis of the vector space over of symmetric functions homog...

Ngày tải lên: 07/08/2014, 06:20

... the poset of graphs ordered by the operations of edge contraction and vertex deletion. (That this poset of graphs does not contain an infinite antichain is a famous theorem of Robertson and Seymour ... well-known terminology of pattern-avoidance, this amounts to saying that p 1 <p 2 if and only if p 1 is a pattern of p 2 . For example, 1 3 2 < 24531aswecandelete 4and...

Ngày tải lên: 07/08/2014, 06:20