Báo cáo toán học: "The Induced Subgraph Order on Unlabelled Graphs" doc

... this notation, we have e(x W → y) = y, W x . 3 The Induced Subgraph Order on Unlabelled Graphs Let V denote the set of isomorphism classes of simple graphs. Define a partial order on V by G ≤ ... The Induced Subgraph Order on Unlabelled Graphs Craig A. Sloss ∗ Department of Combinatorics and Optimization University of Waterloo, Ontario, Canada csloss@math.uwaterloo.ca...

Ngày tải lên: 07/08/2014, 13:21

... c belong to C. The projection p 3 consists in letting all the unit cubes of c fall (in the sense of −e 3 ) on a fixed plane orthogonal to e 3 , as shown on figure 3.5. figure 3.5: projection p 3 The ... be moved. We consider the extremal section s ∗ 3 (c)as a two dimensional polyomino. As such, it is a Ferrers diagram i.e. it belongs to the set F (see the two dimensional projections). The ex...

Ngày tải lên: 07/08/2014, 06:20

... same partition representation. Compositions in an equivalence class may or may not have the same image under D C ; this depends on the distribution of ones in the compositions and the order of the ... can contain multiple cycles, one per connected component of the corresponding directed graph. Definition 2. A partition λ is a Garden of Eden partition or GE-partition if λ has no preimage un...

Ngày tải lên: 07/08/2014, 13:21

... of induced connected subgraphs of K m,n . Proposition 3.2. K m,n has 2 m+n − (2 m + 2 n ) + (m + n + 1) induced connected subgraphs. Proof. Let G = (A, B) = K m,n . For any induced connected subgraph ... 2.6. Let f be an IC-coloring of a graph G, and let G has  induced connected subgraphs. If there are 2k distinct induced connected subgraphs H 1 , G 1 , H 2 , G 2 , · · · , H k ,...

Ngày tải lên: 07/08/2014, 15:23

... operations already performed on some of the facilities) and, subject to this condition, one wishes t o complete the process in the minimum possible time. The concept of excessive [m]-factorization ... generalization of the concept of exces- sive f actorization, introduced by Bonisoli and Cariolaro [1] (an exce s sive fac torization of a graph G is a minimum set o f perfect matchings of G wh...

Ngày tải lên: 08/08/2014, 01:20

... even, but this condition is not sufficient. Sierksma and Hoogeveen [11] summarized seven character- izations. With additional results, these also appear in [7]. The various characterizations have been ... pairs I, J in which one set is empty and the other has size 1, we obtain 0  d i  p(n − 1) for all i, so the induction parameter is positive. When it equals 1, the only realization is the uni...

Ngày tải lên: 08/08/2014, 11:20

... 8: Constructing a component isomorphic to C. Given one of our constructed graphs, there are at most |C|+1 components isomorphic to C, since we have deliberately constructed one and we may have ... a component isomorphic to H. We will now consider the amount of double-counting: Each of our constructed graphs will contain at most 4|H|−e(H)+1 components isomorphic to H (since there were none ......

Ngày tải lên: 08/08/2014, 11:20

Ngày tải lên: 05/08/2014, 10:20

... situation. First, in sec- tion 2.1 , orientations, Eulerian subgraphs and the graph polynomial are discussed. Then, in section 2.2 , vertex colorings are introduced and a new proof of Alon and ... is one column u  and one row e  bigger. We write “under” each column of B a 0 and “behind” each row e ∈ ¯ E the term −X e , on the remaining position “bottom right” we put a 1 . On the “diagon...

Ngày tải lên: 07/08/2014, 13:21

... of subgraphs J ⊆ r · F − is a constant only depending on F and r, this bound holds a.a.s. for all subgraphs J with V (T ) ⊆ V (J) simultaneously. Conditioning on this being the case, we may continue ... 6 Clearly, the vertex v is contained in Base(s 0 ) if X v ≥ 1. We apply Theorem 9 to the family F v in order to obtain a lower bound on the probability of this event. Conditioning on...

Ngày tải lên: 07/08/2014, 21:21