共查询到20条相似文献,搜索用时 31 毫秒
1.
A discrete function f defined on Zn is said to be logconcave if for , , . A more restrictive notion is strong unimodality. Following Barndorff-Nielsen [O. Barndorff-Nielsen, Unimodality and exponential families, Commun. Statist. 1 (1973) 189-216] a discrete function is called strongly unimodal if there exists a convex function such that if . In this paper sufficient conditions that ensure the strong unimodality of a multivariate discrete distribution, are given. Examples of strongly unimodal multivariate discrete distributions are presented. 相似文献
2.
3.
Adrian Kosowski 《Discrete Applied Mathematics》2009,157(2):321-329
Motivated by wavelength-assignment problems for all-to-all traffic in optical networks, we study graph parameters related to sets of paths connecting all pairs of vertices. We consider sets of both undirected and directed paths, under minimisation criteria known as edge congestion and wavelength count; this gives rise to four parameters of a graph G: its edge forwarding index π(G), arc forwarding index , undirected optical index , and directed optical index .In the paper we address two long-standing open problems: whether the equality holds for all graphs, and whether indices π(G) and are hard to compute. For the first problem, we give an example of a family of planar graphs {Gk} such that . For the second problem, we show that determining either π(G) or is NP-hard. 相似文献
4.
Two classes of edge domination in graphs 总被引:2,自引:0,他引:2
Baogen Xu 《Discrete Applied Mathematics》2006,154(10):1541-1546
Let (, resp.) be the number of (local) signed edge domination of a graph G [B. Xu, On signed edge domination numbers of graphs, Discrete Math. 239 (2001) 179-189]. In this paper, we prove mainly that and hold for any graph G of order n(n?4), and pose several open problems and conjectures. 相似文献
5.
6.
7.
8.
Jin-Hui Fang 《Discrete Applied Mathematics》2008,156(15):2950-2958
It is conjectured by Erd?s, Graham and Spencer that if 1≤a1≤a2≤?≤as are integers with , then this sum can be decomposed into n parts so that all partial sums are ≤1. This is not true for as shown by a1=?=an−2=1, . In 1997 Sandor proved that Erd?s-Graham-Spencer conjecture is true for . Recently, Chen proved that the conjecture is true for . In this paper, we prove that Erd?s-Graham-Spencer conjecture is true for . 相似文献
9.
Jonathan Lenchner 《Discrete Applied Mathematics》2011,159(7):612-620
10.
Improved bounds for acyclic chromatic index of planar graphs 总被引:1,自引:0,他引:1
11.
12.
While connected arithmetic discrete lines are entirely characterized, only partial results exist for the more general case of arithmetic discrete hyperplanes. In the present paper, we focus on the three-dimensional case, that is on arithmetic discrete planes. Thanks to arithmetic reductions on a vector , we provide algorithms either to determine whether a given arithmetic discrete plane with as normal vector is connected, or to compute the minimal thickness for which an arithmetic discrete plane with normal vector is connected. 相似文献
13.
14.
Sachin Gautam Ashish Kumar Srivastava Amitabha Tripathi 《Discrete Applied Mathematics》2008,156(12):2423-2428
Given graphs , where k≥2, the notation
15.
For a given structure D (digraph, multidigraph, or pseudodigraph) and an integer r large enough, a smallest inducing r-regularization of D is constructed. This regularization is an r-regular superstructure of the smallest possible order with bounded arc multiplicity, and containing D as an induced substructure. The sharp upper bound on the number, ρ, of necessary new vertices among such superstructures for n-vertex general digraphs D is determined, ρ being called the inducing regulation number of D. For being the maximum among semi-degrees in D, simple n-vertex digraphs D with largest possible ρ are characterized if either or (where the case is not a trivial subcase of ). 相似文献
16.
17.
Quadratic minimisation problems in statistics 总被引:1,自引:0,他引:1
18.
19.
20.
We improve parts of the results of [T. W. Cusick, P. Stanica, Fast evaluation, weights and nonlinearity of rotation-symmetric functions, Discrete Mathematics 258 (2002) 289-301; J. Pieprzyk, C. X. Qu, Fast hashing and rotation-symmetric functions, Journal of Universal Computer Science 5 (1) (1999) 20-31]. It is observed that the n-variable quadratic Boolean functions, for , which are homogeneous rotation symmetric, may not be affinely equivalent for fixed n and different choices of s. We show that their weights and nonlinearity are exactly characterized by the cyclic subgroup 〈s−1〉 of Zn. If , the order of s−1, is even, the weight and nonlinearity are the same and given by . If the order is odd, it is balanced and nonlinearity is given by . 相似文献