Báo cáo toán học: " Alspach’s Problem: The Case of Hamilton Cycles and 5-Cycles" pps

... decomposition of [1, n 4 − k − 1] ∪ { n 4 } n into n 4 − k Hamilton cycles. We now consider the case of Hamilton cycles and 5 -cycles. The proof of this result when n is odd splits into 2 cases, namely ... h and t with hn + 5t = n(n− 2)/2, the complete graph K n decomposes into h Hamilton cycles, t 5 -cycles, and a 1-factor. We also settle Alspach’s problem...

Ngày tải lên: 08/08/2014, 14:23

... arguments justify the other relations. These lemmas have proved that the disposition of the red, blue, green, and yellow points in the graph of a skew-merged permutation σ is as given in Theorem 1. The next ... the other statements follow by symmetry. To complete the proof of Theorem 1 we have Lemma 7 The white points of a permutation are either increasing or de- cre...

Ngày tải lên: 07/08/2014, 06:22

... removing the first row and the j’th column (j = 1, 2, . . . , d+1) of A x . By the definition of T we see that the adjacency matrix of D is exactly T. By Stanley [6, Theorem 4.7.2], the right hand side ... x 2 ). On the o ther hand, if x ′  y ′ , then x 2  y 2 and d − 1 − a  d − 1 − b  d − 1 − y 2 < d − y 2 and so x ′ ∈ Y x 2 ,d−y 2 and (y ′ , x ′ ) ∈ Z 2 . Subc...

Ngày tải lên: 08/08/2014, 01:20

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Ngày tải lên: 05/08/2014, 15:20

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Ngày tải lên: 05/08/2014, 09:46

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Ngày tải lên: 05/08/2014, 15:20

... class="bi x0 y1 w2 h 2" alt =""

Ngày tải lên: 05/08/2014, 15:21

... Denote by SF n k, the number of (k, )-sum-free subsets of [1,n]. Since the set of 1 the electronic journal of combinatorics 7 (2000), #R30 7 Proof. We need to show that the left-hand side of (4) is ... ϕ r )2 n/ρ +2n 2 2 n/(ρ+1) . To complete the proof it is sufficient to show that the number of (k, )- sum-free subsets of [1,n] satisfying either (1) or (2) is o(2...

Ngày tải lên: 07/08/2014, 06:20

... field, and let r F (M) denote the rank of M over F . Theorem. If (k − t) =0inthefieldF ,then r F (W t,k (v +1))=r F (W t,k−1 (v)) + r F ((k − t +1)W t−1,k (v)). (1) Proof. The block-matrix identity  I ... relation is derived for the rank (over most fields) of the set-inclusion matrices on a finite ground set. Given a finite set X of say v elements, let W = W t,k (v) be the (0,1...

Ngày tải lên: 07/08/2014, 06:22