Báo cáo toán học: "On Universal Cycles of Labeled Graphs" ppt

... notion of universal cycles. In particular, we show that these cycles exist for certain classes of labeled graphs. In order to define a universal cycle of graphs, we must first extend the notion of ... Classification: 05C30 Abstract A universal cycle is a compact listing of a class of combinatorial objects. In this paper, we prove the existence of universal cycles of...

Ngày tải lên: 08/08/2014, 11:20

Ngày tải lên: 05/08/2014, 15:21

Ngày tải lên: 05/08/2014, 15:21

... the proof. Proof of Theorem 2: Suppose that Λ, M ⊆ A are maximal dissociated subsets of A. By maximality of Λ, every element of A, and consequently every element of M, is a linear combination of ... the element of M, and therefore every maximal dissociated subset of A is a singleton, too ) , we assume |M| ≥ 2 below. Since every element of Λ is a linear combination of the e...

Ngày tải lên: 08/08/2014, 14:23

... R, P ⊂ R and PK ⊂ K the set of reduced cycles, primitive, reduced cycles and primitive cycles of G, respectively. Also, primitive, reduced cycles are called prime cycles. Let C m , C nontail m , ... journal of combinatorics 16 (2009), #R30 9 Proof. The first formula is clear. We prove the second formula. The proof is an analogue of the proof of Lemma 1 in [21]. We count the p...

Ngày tải lên: 07/08/2014, 21:21

... d(v 2 ), , d(v n )) denotes the diagonal matrix of vertex degrees of G, and d(v) denotes the degree of the vertex v of G. The Laplacian spectrum of G can be denoted by SL(G) = (µ 1 (G), µ 2 (G), ... following proofs. Let G be a graph and let v be a vertex of G . The neighborhood of v in G is denoted by N(v), i.e. N(v) = {w : wv ∈ E(G)}. Denote by ∆(G) the maximum degree of all...

Ngày tải lên: 07/08/2014, 21:21

... is a pair of cycles of lengths a and b + c; 4. for at most n i choices, C i ⊕C is a pair of cycles of lengths c and a + b; 5. for at most n i choices, C i ⊕C is a triple of cycles of lengths ... argue the existence of a 6-cycle as in the previous case. Remark: The proof shows that the number of Hamilton cycles is within a poly- nomial factor of the number of two fa...

Ngày tải lên: 07/08/2014, 06:22

... 0, 0 ≤ j ≤ n. Then the solution of (4.4) and (4.5) is bounded if and only if the condition (5.5) is satisfied. Proof. The proof is immediate consequence from proof of Theorem 4.3 with Remark 5.1. Remark ... condition for the boundedness of all solutions of (1.1) and the scalar case of (1.1), respectively. The next result provides a sufficient condition for the boundedness of solution...

Ngày tải lên: 20/06/2014, 20:20

... for PAPR distri- bution of OFDM/TDM signal and then, we develop the expression for the capacity of OFDM/TDM using MMSE-FDE. A. PAPR of OFDM/TDM The baseband oversampled OFDM/TDM signal given by (2) ... PAPR problem of conventional OFDM at the cost of slight decrease in spect rum efficiency. The capacity of OFDM/ TDM using MMSE-FDE is o btained based on the Gaus- sian assumption o...

Ngày tải lên: 20/06/2014, 21:20

Ngày tải lên: 05/08/2014, 10:20