Báo cáo toán học: "The t-pebbling number is eventually linear in t " pptx

... pebbling moves leading to a distibution with at least t pebbles at x. Answering a question of Sieben, we show that for every graph G, π t (G) is eventually linear in t; that is, there are numbers ... claim that, starting with p 0 , it is impossible to obtain t pebbles at x. To check this, we define the potential of a pebbling distribution p as F (p) :=  v∈V (G) p(v) mdist(v,...

Ngày tải lên: 08/08/2014, 14:23

... get a contribution to the permanent). Thus the square of the number of perfect matchings is at most the permanent of the adjacency matrix, and the desired inequality follows from Bregman-Minc ... Bregman-Minc by taking the square root of (2.1), where the numbers r i are the degrees of the vertices of G. It is clear that if G is a vertex-disjoint union of balanced complete bipartite gr...

Ngày tải lên: 07/08/2014, 15:22

... eliminating at most two thirds of the cycles in C \ C 0 , we are left with a collection C  of pairwise nonhomotopic, simple closed curves that pairwise intersect in exactly one point. By [8], there ... pairwise intersect in exactly one point, unless some point belongs to more than two curves. Since C is an I–collection, it follows that no four curves in C \C 0 are pairwise homotopi...

Ngày tải lên: 07/08/2014, 15:23

... − 2 ¯ d(G) 3  . Thus Theorem 1 shows that provided the minimal degree is not too small, there is a large independent set in the graph. In particular, we may apply this result to thecasewhenG is a regular ... a breakthrough in this area when they provided a polynomial algorithm to find an independent set of size at least α(G) ≥ n log d 100d . * Correspondence to Tristan Denley, Mat...

Ngày tải lên: 07/08/2014, 06:20

... to n.LetA (respectively B) be the set of vertices v of G such that the minimum label on vertices at distance k or less from v is at even (respectively odd) distance k − 1orless. It is easy to see that ... 1). Since the arithmetic mean is greater than the geometric mean, we can conclude that α(G) ≥  v∈G  d 1 (v)2 −(k−2) 1+d 1 (v)+···+ d k (v)  1/k−1 . Since the points at even (odd) di...

Ngày tải lên: 07/08/2014, 06:20

... it is an in ection point for g (t) , which therefore remains strictly increasing for all t s. If β< 2 3 √ 3 , then there are two roots 0 <τ 0 <k/3<τ 1 <1, so that g (t) is increasing ... x>0andm+1−k>ω 3 (n), then by (3.7)  t ω(n) [m +1−k +t] t m t p (t, k t) ≤  t ω(n) (1 − x/2) t p (t) = o(1). Note that  t& lt;ω(n) [m +1−k +t] t m t p (t, k t) ∼ ...

Ngày tải lên: 07/08/2014, 06:20

... to see that this condition is equivalent to the permutation being divisible into (at most) k disjoint monotone descending subsequences, or k disjoint monotone ascending subsequences. If it can ... adjacent. It is easy to see that Theorem 4 is a correct characterisation of extremal sequences with that property. Lemma 5 Suppose n>2 and that some extremal permutation has 0 and n − 1 adj...

Ngày tải lên: 07/08/2014, 07:21

... just need to make sure that the short paths do not intersect and they do not interfere with the long paths. This will be guaranteed by the introduction of the set B in the lemmas below. This plan ... proved in [18] that R(C 3 n , C 3 n ) is asymptotic to 5n/4. In this paper we extend that result by showing that for r ≥ 3, R(C r n , C r n ) is asymptotic to (2r−1)n 2r−2 . To see that...

Ngày tải lên: 07/08/2014, 21:20

... d(v 4 ). Let |A| denote the cardinality of the set A. If F is a graph then V (F ) denotes its vertex set. The neighborhood N F (v) of a vertex v is the set of vertices adjacent to v in the graph ... denote the set of all graphs G of order n, such that G does not contain G 1 and G does not contain G 2 , where G is the complement of G. The Ramsey number r(G 1 , G 2 ) is the smallest...

Ngày tải lên: 08/08/2014, 14:23

... indeed the next step in clinical investigation, but not quite ready for implementation into clinical practice before the hypothesis is definitively investigated in a controlled trial. Conclusion ... an ischemic stroke. The results of the present study and ensuing discussion may tempt one to surmise that blood pressure variability is bad and that therefore somehow tightly contr...

Ngày tải lên: 20/06/2014, 20:20