Báo cáo toán học: "On Directed Triangles in Digraphs" pps

... the resulting digraph D  is acyclic. If true, this conjecture would imply the following strengthening of Lemma 5: Each digraph D obtained from a tournament by deleting k edges, that has no directed triangles, has ... with minimum outdegree at least αn has a directed 3-cycle. Theorem 3. If β ≥ 0.34564, then each n-vertex digraph D in which both minimum outdegree and minimum indegree i...

Ngày tải lên: 07/08/2014, 13:21

Ngày tải lên: 05/08/2014, 15:20

... arithmetical analysis which appeared in Chinese [6] in 1988 and in English [7] in 1989. In the following result, we prove that any set of p non-negative integers s 1 ,s 2 , ,s p with s 1 <s 2 < ... the inequalities in the above mentioned formula for those values of k,forwhichs k <s k+1 hold, need to be checked [5, p.608]. The following results can be seen in [5]. Theore...

Ngày tải lên: 06/08/2014, 05:20

... elementary construction using binary codes gives new record kissing numbers in dimensions from 32 to 128. 1. Introduction Let τ n denote the maximal kissing number in dimension n, that is, the ... 30,828. In this way we obtain a kissing number of 331,737,984. n=80. By taking 4 orbits under L 2 (79) we obtain A(80, 16, 16) ≥ 143,780. We take n 0 = 64, n 1 = 16, n 2 =4,n 3 = 1 and obtain...

Ngày tải lên: 07/08/2014, 06:22

... us in (1) k(|D|−|S|)+d|S|−q +2≤ e G (D, S) ≤ d|D|−q, leading to (d − k)(|D|−|S|) ≥ 2. ✷ Proof of Theorem 1.1. The first case follows from the well-known Theorem of Petersen [6]. In the remaining ... disjoint subsets D, S of V (G), whether G has a k-factor or not. In 1985, Enomoto, Jackson, Katerinis and Saito [3] proved the following result. Lemma 2.2 Let G be a graph and k a positive in...

Ngày tải lên: 07/08/2014, 08:20

... two non-codewords in F(i, j) are in the lower-left and upper-right corners (in the other case, we just go up instead of going down in what follows: as explained above, the voting rule is symmetric in this ... Lobstein, The minimum density of an identifying code in the king lattice, Discrete Math. 276 (2004), pp. 95–109. [5] I. Charon, O. Hudry and A. Lobstein, Extremal cardinalitie...

Ngày tải lên: 07/08/2014, 15:22

... precisely in one of d − 2 open intervals  k d , k+1 d  , where k = 1, . . . , d − 2. Indeed, neither two terms of  j δ  δ−1 j=1 nor two terms of  j d−δ  d−δ−1 j=1 are in the same interval since ... decreasing (resp. increasing), and so the log-concavity implies the unimodality. The unimodality problems, including concavity (convexity) and log- concavity (log-convexity), arise natura...

Ngày tải lên: 07/08/2014, 21:20

... cent to v 1 in Avo ider’s graph at this point. For 2  i  k, in the beginning of the i- t h subphase, Avoider chooses the vertex v i ∈ V i−1 of minimal degree in Enfor cer’s graph induced on ... found in [9]. 1.1 Preliminaries The theory behind Avoider-Enforcer games is less developed than the one behind Maker- Breaker games. However, when it comes to determining how fast can Enforce...

Ngày tải lên: 08/08/2014, 12:22

... O(L −1 ). Inserting this expression into the previous equality and integrating we obtain the desired result (10). To prove (11 ) , we first restrict the region to 1  k  √ m where all obtained remainder term ... these results can be used to obtain asymptotical formulas for max mk d k (m) as k → ∞. We intend to discuss that in a forthcoming paper. 2 The saddle point method Since P m (k) = q...

Ngày tải lên: 08/08/2014, 12:22

Ngày tải lên: 05/08/2014, 09:46