Báo cáo toán học: "A note on packing chromatic number of the square lattice" ppsx

... y. Furthermore, let W denote the set of neighbours of y. Consider a graph G ′′ := G − {y, z}. Thus W consists of l vertices of degree  1 in G ′′ and one vertex of degree k  l in G ′′ . Note ... (xσ ′ (v)yσ ′ (w))σ ′ is a packing of G and in the latter case (xσ ′ (v))(yσ ′ (w))σ ′ is a packing of G. Thus we get a contradiction. Assume now that G ′ − U is a star (with...

Ngày tải lên: 07/08/2014, 21:21

... the condition nP(|X 1 | > η n ) ≤ c(log n) ε 0 , 0 < ε 0 < 1 in theorem 1.1 of [12]. Remark 1.4. If EX 2 < ∞, then X is in the domain of attraction of the normal law. Therefore, the ... of random variables in the domain of attraction of the normal law, we will show that the ASCLT holds under a fairly general growth condition on d k = k −1 exp(ln k) α ),...

Ngày tải lên: 20/06/2014, 21:20

Ngày tải lên: 05/08/2014, 10:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:21

... the first question for all k ≥ 4 and to the second question for all k ≥ 5. We would like to note that there is an interesting discussion about the Burkard–Hammer condition in [9]. Concerning the ... Formulations of the Main Results and Discussions By Theorem 2 in the previous section there are no nonhamiltonian Burkard– Hammer graphs G = S(I ∪ K, E)withδ(G) ≥|I|−2 and no nonham...

Ngày tải lên: 06/08/2014, 05:20

... need only show that no prefix of m n is an overlap. First note that no prefix of m n is a square of length 12 or greater; otherwise the prefix of m n of length 6 reappears internally, i.e. m n contains ... finite string of letters from Σ. The length of word w is the number of letters in w, denoted by |w|. Thus |banana| = 6, for example. The language consisting of a...

Ngày tải lên: 07/08/2014, 06:20

... row-span of this table. Since the dimension of the row-span of a matrix is equal to the dimension of its column-span, we can equally well study the dimension of the space spanned by the columns of the ... the reflection representation of a finite Coxeter group. This is essentially what we are looking at. (The defining representation of S n consists of the dir...

Ngày tải lên: 07/08/2014, 06:20

... ,ω. Proof To prove the lemma we are going to use the Janson inequality, cf. [1] for notation. Note that the number of choices of (ω,γ)-partitions of an n-set is at most  n γ  (eω) N . the electronic ... two long edges in  C in both directions along the cycle. If the short edges of C all have the same label and they make up more than one subpath then the paths o...

Ngày tải lên: 07/08/2014, 06:20

... conditioning on the event C P 0 , the random graphs of the resulting probability space may contain edges only from within the edges that connect vertices of different partitions of P 0 . The number ... information on Maple) implementation of the downhill simplex function optimization method (see [13] for a good description of the method and a C implementation) to...

Ngày tải lên: 07/08/2014, 06:20