共查询到20条相似文献,搜索用时 12 毫秒
1.
Pablo Coll Javier Marenco Isabel Méndez Díaz Paula Zabala 《Annals of Operations Research》2002,116(1-4):79-90
In this paper we present a study of the polytope associated to a classic linear integer programming formulation of the graph coloring problem. We determine some families of facets. This is the initial step for the development of a branch-and-cut algorithm to solve large instances of the graph coloring problem. 相似文献
2.
Dedicated to the memory of Paul Erdős
A facet of the stable set polytope of a graph G can be viewed as a generalization of the notion of an -critical graph. We extend several results from the theory of -critical graphs to facets. The defect of a nontrivial, full-dimensional facet of the stable set polytope of a graph G is defined by . We prove the upper bound for the degree of any node u in a critical facet-graph, and show that can occur only when . We also give a simple proof of the characterization of critical facet-graphs with defect 2 proved by Sewell [11]. As an
application of these techniques we sharpen a result of Surányi [13] by showing that if an -critical graph has defect and contains nodes of degree , then the graph is an odd subdivision of .
Received October 23, 1998 相似文献
3.
We give a new lower bound for the rectilinear crossing number of the complete geometric graph Kn. We prove that and we extend the proof of the result to pseudolinear drawings of Kn.
Dedicated to the memory of our good friend and mentor Víctor Neumann-Lara.
Received: April, 2003
Final version received: March 18, 2005 相似文献
4.
In this paper the authors use a modified Wirtinger presentation to give a lower bound on the unknotting number of a knot in S3. 相似文献
5.
Roman N. Karasev 《Discrete and Computational Geometry》2005,34(1):25-45
Three theorems of this paper generalize previous results of the author
on conjectures of A. Bezdek and V.V. Proizvolov. They show the existence of mappings from a given point set to the set of facets of a given polytope that satistfy some special conditions. Developing the same technique, some results on convex polytope partitions are presented, two of them dealing with partitions with prescribed measures of parts. Then we prove a corollary on the existence of a possibly nonconvex polytope with a given set of vertices, containing given points in its interior. We also consider problems of the following type: find an assignment of vectors from a given set to the parts of a given convex partition of ℝn so that the shifts of the parts by their corresponding vectors either do not intersect by interior points or cover ℝn 相似文献
6.
V. V. Tarkaev 《Siberian Mathematical Journal》2018,59(6):1125-1132
We introduce the notion of homological multiplicity for an oriented link in a thickened orientable closed surface. Using the notion, we establish some lower bounds for the crossing number of a link in thickened surfaces. 相似文献
7.
关于Ramsey数下界的部分结果 总被引:3,自引:1,他引:2
刘富贵 《数学的实践与认识》2002,32(1):97-99
本文得到 Ramsey数下界的一个计算公式 :R( l,s+ t-2 )≥ R( l,s) + R( l,t) -1 ,(式中 l、s、t≥ 3) .用此公式算得的 Ramsey数的下界比用其它公式算得的下界好 . 相似文献
8.
We investigate how the algebraic connectivity of a graph changes by relocating a connected branch from one vertex to another vertex, and then minimize the algebraic connectivity among all connected graphs of order n with fixed domination number \(\gamma\leq\frac{n+2}{3}\), and finally present a lower bound for the algebraic connectivity in terms of the domination number. We also characterize the minimum algebraic connectivity of graphs with domination number half their order. 相似文献
9.
A nonincreasing sequence π=(d1,…,dn) of nonnegative integers is a graphic sequence if it is realizable by a simple graph G on n vertices.In this case,G is referred to as a realization of π.Given a graph H,a graphic sequence π is potentially H-graphic if π has a realization containing H as a subgraph.For graphs G1 and G2,the potential-Ramsey number rpot(G1,G2) is the smallest integer k such that for every k-term graphic ... 相似文献
10.
Vasilios I. Manousiouthakis Neil Thomas Ahmad M. Justanieah 《Journal of Optimization Theory and Applications》2011,151(1):121-134
In this paper, a finite branch-and-bound algorithm is developed for the minimization of a concave power law over a polytope.
Linear terms are also included in the objective function. Using the first order necessary conditions of optimality, the optimization
problem is transformed into an equivalent problem consisting of a linear objective function, a set of linear constraints,
a set of convex constraints, and a set of bilinear complementary constraints. The transformed problem is then solved using
a finite branch-and-bound algorithm that solves two convex problems at each of its nodes. The method is illustrated by means
of an example from the literature. 相似文献
11.
Jarod Alper Tristram Bogart Mauricio Velasco 《Foundations of Computational Mathematics》2017,17(3):829-836
We prove that the determinantal complexity of a hypersurface of degree \(d > 2\) is bounded below by one more than the codimension of the singular locus, provided that this codimension is at least 5. As a result, we obtain that the determinantal complexity of the \(3 \times 3\) permanent is 7. We also prove that for \(n> 3\), there is no nonsingular hypersurface in \({\mathbb {P}}^n\) of degree d that has an expression as a determinant of a \(d \times d\) matrix of linear forms, while on the other hand for \(n \le 3\), a general determinantal expression is nonsingular. Finally, we answer a question of Ressayre by showing that the determinantal complexity of the unique (singular) cubic surface containing a single line is 5. 相似文献
12.
Dennis Eichhorn 《Annals of Combinatorics》2009,13(3):297-303
The parity of p(n), the ordinary partition function, has been studied for at least a century, yet it still remains something of a mystery.
Although much work has been done, the known lower bounds for the number of even and odd values of p(n) for n ≤ N still appear to have a great deal of room for improvement. In this paper, we use classical methods to give a new lower bound
for the number of odd values of p(n). 相似文献
13.
14.
Mathematical Notes - An upper bound for the number of field elements that can be taken to roots of unity of fixed multiplicity by means of several given polynomials is obtained. This bound... 相似文献
15.
Let a,b be given, multiplicatively independent positive integers and let >0. In a recent paper jointly with Y. Bugeaud we proved the upper bound exp(n) for g.c.d.(an–1, bn–1); shortly afterwards we generalized this to the estimate g.c.d.(u–1,v–1)<>u,v) for multiplicatively independent S-units u,vZ. In a subsequent analysis of those results it turned out that a perhaps better formulation of them may be obtained in terms of the language of heights of algebraic numbers. In fact, the purposes of the present paper are: to generalize the upper bound for the g.c.d. to pairs of rational functions other than {u–1,v–1} and to extend the results to the realm of algebraic numbers, giving at the same time a new formulation of the bounds in terms of height functions and algebraic subgroups of Gm2. 相似文献
16.
Rolf S. Rees 《Journal of Combinatorial Theory, Series A》2000,90(2):257
A truncated transversal design TTD of type gkm1 is a {k, k+1}-GDD of type gkm1 in which each point on the group of size m lies only in blocks of size k+1. Thus a TTD of type gkm1 is equivalent to a transversal design TD (k, g) having m disjoint parallel classes of blocks. We employ a new construction developed by the author (1993, J. Combin. Des.1, 15–26) to show that if g1<g2 and if there exists a TD (k, g1) and a TD (k+1, g2), then there exists a TTD of type (g1g2)km1 for any 0m(g2 div g1) g21. As a corollary, we obtain a new lower bound on the number of mutually orthogonal idempotent latin squares of side g: if g1<g2 and there exist r MOLS of side g1 and r+1 MOLS of side g2 , then N(1 g1g2)r. 相似文献
17.
关于《关于Ramsey数下界的部分结果》的注 总被引:1,自引:0,他引:1
张忠辅 《数学的实践与认识》2002,32(4):686
本文用反例 ,说明了 [1 ]中 R( l,s+ t-2 ) R( l,s) + R( l,t) -1是错的 相似文献
18.
We revisit the method of Chvátal, Cook, and Hartmann to establish lower bounds on the Chvátal-Gomory rank, and develop a simpler method. We provide new families of polytopes in the 0/1 cube with high rank, and we describe a deterministic family achieving a rank of at least (1+1/e)n−1>n. Finally, we show how integrality gaps lead to lower bounds. 相似文献
19.
G. Grätzer, H. Lakser, and E. T. Schmidt proved that every finite distributive lattice D with n join-irreducible elements can be represented as the congruence lattice of a lattice L with O(n2) elements. G. Grätzer, I. Rival, and N. Zaguia gave kn, < 2, as a lower bound for the size of such a lattice L; a sharper form, 1/64(n/log2n)2, of this result was given by Y. Zhang.In this note, we apply a recent result of R. Freese, to obtain 1/16 n2/log2n as a lower bound. We also give a direct proof of Freese's result. 相似文献
20.
For a connected graph G, the distance d(u, v) between two vertices u and v is the length of a shortest u − v path in G and the distance d(v) of a vertex v is the sum of the distances between v and all vertices of G. The margin, μ (G), is the subgraph induced by vertices of G having the maximum distance. It is known that every graph is isomorphic to the margin of some graph H. For a graph G, the marginal appendage number is defined as min{p(H) − p(G) ∣ μ(H) = G}. In this paper it is shown that Δ (G) + 2 is a sharp bound for the marginal appendage number. 相似文献