Báo cáo toán học: "Edge and total choosability of near-outerplanar graphs" ppsx

... W. Wang and K W. Lih, Choosability, edge choosability, and total choosability of outerplane graphs, European J. Combin 22 (2001), 71–78. [10] D. R. Woodall, A short proof of a theorem of Dirac’s ... vertices of degree 2, by Theorem 1.3. This contradiction completes the proof of Theorem 1.2. ✷ the electronic journal of combinatorics 13 (2006), #R98 6 Edge and total c...

Ngày tải lên: 07/08/2014, 13:21

... Z-labelling of G. We introduce the following notation: • H V denotes the set of labels of the Vertices of H. • H E denotes the set of labels of the Edges of H. • B E denotes the set of labels of the ... between ν and ν  and no elements of B E ∪ H V can lie between them as such labels come in intervals of (b − a) + 1 integers. We are now ready to complete the proof...

Ngày tải lên: 07/08/2014, 13:21

... respectively the set of successors of v,the set of predecessors of v and the set of neighbors of v in G.Themaximum degree and minimum degree of a graph G are respectively denoted by ∆(G )and (G). We denote ... arcs of A  . Let G be an oriented graph and f be an oriented arc-coloring of G. For a given vertex v of G,wedenotebyC + f (v)andC − f (v) the outgoing color s...

Ngày tải lên: 07/08/2014, 13:21

... one of the graphs of type A in Fig. 1, and this completes the proof. ✷ Lemma 10 Let G be an incompatible graph and suppose λ ∗ (G) = 3. Then G is isomorphic to a graph of type B of Fig. 1. Proof. ... e and f ′ and at least 3 edges joining e ′ and f. This implies the existence of the edges pz and ry, respectively. The only other admissible edges are one edge of the form...

Ngày tải lên: 08/08/2014, 01:20

... 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 ... full incorporation of the TiO 2 and ZrO 2 film, as shown in TEM. Figure 2 High-resolution cross-sectional TEM images of the interface between the composite thin films and Si.(...

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

... 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 15. If G O has a vertex of degree ... vertex of degree two and either connected or two-connected. By Lemma 13 and Lemma 14 there is a subset of vertices V 1 and a component G 1 of G O \V 1 such that G 1 ∪V...

Ngày tải lên: 07/08/2014, 13:21

... 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