Báo cáo toán học: "The Planarity Theorems of MacLane and Whitney for Graph-like Continua" pdf

... planar dual of G and let C be a cycle of G. Lemma 3.2 implies that the subgraphs of H on either s ide of C are connected and, therefore, the edges of H dual to the edges of C form a bond of H. To ... journal of combinatorics 17 (2010), #R12 8 The Planarity Theorems of MacLane and Whitney for Graph-like Continua Robin Christian, R. Bruce Richter, Brendan Ro o...

Ngày tải lên: 08/08/2014, 11:20

Ngày tải lên: 05/08/2014, 09:46

Ngày tải lên: 05/08/2014, 10:20

Ngày tải lên: 05/08/2014, 10:20

Ngày tải lên: 05/08/2014, 10:20

... of S,thenλ 1 = λ 2 if and only if λ 1 e = λ 2 e for all e ∈ E. (ii) If ρ 1 and ρ 2 are right translations of S,thenρ 1 = ρ 2 if and only if eρ 1 = eρ 2 for all e ∈ E. Proof. We only need to show ... the mappings λ + and ρ + which map S into itself by aρ + = a(λa + ) + and λ + a =(λa + ) + a, for all a ∈ S. For the mappings λ + and ρ + , we have the following lemma. Lem...

Ngày tải lên: 06/08/2014, 05:20

... 2.14. For 0 ≤ s ≤ d− < 2j + u − 1 > − −1, the elements X s K u,j and X s  F u,j are linearly independent. Proof. The proof of this lemma is same to the proof of Lemma 2.18 in [7]. For completeness, ... is a kind of generalization of gener- alized Taft algebra and of course Taft algebra. Therefore, it is natural to ask the following question: whether is the quantum dou...

Ngày tải lên: 06/08/2014, 05:20

... similar results for graphs which are not regular. Using these results we improve on the lower bound of Monien and Speckenmeyer, for the independence number of a graph of order n and odd girth 2k ... bounds for the independence number of general graphs of a given odd girth. We shall prove some similar bounds to those we prove for regular graphs in terms of a measure of...

Ngày tải lên: 07/08/2014, 06:20

... average degree of vertices of G.Then α(G) ≥  n ¯ d/2. Proof. Since G contains no 3 or 5 cycles, we have α(G) ≥ d 1 (v) (consider the neighbors of v )and (G) ≥ 1+d 2 (v) (consider v and the points ... d k−1 (v)) 1+d 1 (v)+···+ d k (v) . Proof. Randomly label the vertices of G with a permutation of the integers from 1 to n.LetA (respectively B) be the set of vertices v of G suc...

Ngày tải lên: 07/08/2014, 06:20

... other hand. For most values of n, we shall use elementary estimates and some well-known bounds for ordinary partitions (of a number) to express most values of b n in terms of the number of ordinary ... e G(t 0 ) ·  2π −G  (t 0 ) . the electronic journal of combinatorics 6 (1999), #R2 13 3. Structure of Proof The propositions and theorems are proved in this section,...

Ngày tải lên: 07/08/2014, 06:20