34447441
Asymptotic bounds for some bipartite graph: complete graph Ramsey numbers
Abstract The Ramsey number r(H,Kn) is the smallest integer N so that each graph on N vertices that fails to contain H as a subgraph has independence number at least n. It is shown that r(K 2,m ,K n )⩽(m−1+ o (1))(n/ log n) 2 and r(C 2m ,K n )⩽c(n/ log n) m/(m−1) for m fixed and n→∞. Also r(K 2,n ,K n )=Θ(n 3 / log 2 n) and r(C 5 ,K n )⩽cn 3/2 / log n .
2037433
An upper bound for ramsey numbers
Let G″ be a graph obtained from G by deleting two vertices. It is shown that r(G, H) ⩽ A + B + 2 + 2 (A2 + AB + B2)3 where A = r(G″, H) and B = r(G,H″).
206570728
On Book-Complete Graph Ramsey Numbers
It is shown that a graph of orderNand average degreedthat does not contain the bookBm=K1+K1, mas a subgraph has independence number at leastNf(d), wheref(x)~(logx/x)(x?∞). From this result we find that the book-complete graph Ramsey number satisfiesr(Bm, Kn)?mn2/log(n/e). It is also shown that for every treeTmwithmedges,r(K1+Tm,Kn)?(2m?1)n2/log(n/e).
34644814
The Independence Number of Graphs with a Forbidden Cycle and Ramsey Numbers
Let k ≥ 5 be a fixed integer and let m = ⌊(k − 1)/2⌋. It is shown that the independence number of a Ck-free graph is at least c1[∑ d(v)1/(m − 1)](m − 1)/m and that, for odd k, the Ramsey number r(Ck, Kn) is at most c2(nm + 1/log n)1/m, where c1 = c1(m) > 0 and c2 = c2(m) > 0.
206964202
Asymptotic Upper Bounds for Ramsey Functions
Abstract. We show that for any graph G with N vertices and average degree d, if the average degree of any neighborhood induced subgraph is at most a, then the independence number of G is at least Nfa+1(d), where fa+1(d)=∫01(((1−t)1/(a+1))/(a+1+(d−a−1)t))dt. Based on this result, we prove that for any fixed k and l, there holds r(Kk+l,Kn)≤ (l+o(1))nk/(logn)k−1. In particular, r(Kk, Kn)≤(1+o(1))nk−1/(log n)k−2.
8083367
On Some Three-Color Ramsey Numbers
Abstract. In this paper we study three-color Ramsey numbers. Let Ki,j denote a complete i by j bipartite graph. We shall show that (i) for any connected graphs G1, G2 and G3, if r(G1, G2)≥s(G3), then r(G1, G2, G3)≥(r(G1, G2)−1)(χ(G3)−1)+s(G3), where s(G3) is the chromatic surplus of G3; (ii) (k+m−2)(n−1)+1≤r(K1,k, K1,m, Kn)≤ (k+m−1)(n−1)+1, and if k or m is odd, the second inequality becomes an equality; (iii) for any fixed m≥k≥2, there is a constant c such that r(Kk,m, Kk,m, Kn)≤c(n/logn), and r(C2m, C2m, Kn)≤c(n/logn)m/(m−1) for sufficiently large n.
372272
Data-Driven Grasp Synthesis Using Shape Matching and Task-Based Pruning
Human grasps, especially whole-hand grasps, are difficult to animate because of the high number of degrees of freedom of the hand and the need for the hand to conform naturally to the object surface. Captured human motion data provides us with a rich source of examples of natural grasps. However, for each new object, we are faced with the problem of selecting the best grasp from the database and adapting it to that object. This paper presents a data-driven approach to grasp synthesis. We begin with a database of captured human grasps. To identify candidate grasps for a new object, we introduce a novel shape matching algorithm that matches hand shape to object shape by identifying collections of features having similar relative placements and surface normals. This step returns many grasp candidates, which are clustered and pruned by choosing the grasp best suited for the intended task. For pruning undesirable grasps, we develop an anatomically-based grasp quality measure specific to the human hand. Examples of grasp synthesis are shown for a variety of objects not present in the original database. This algorithm should be useful both as an animator tool for posing the hand and for automatic grasp synthesis in virtual environments.
12666680
Semantic Web Languages - Towards an Institutional Perspective
The Semantic Web (SW) is viewed as the next generation of the Web that enables intelligent software agents to process and aggregate data autonomously. Ontology languages provide basic vocabularies to semantically markup data on the SW. We have witnessed an increase of numbers of SW languages in the last years. These languages, such as RDF, RDF Schema (RDFS), the OWL suite of languages, the OWL− − suite, SWRL, are based on different semantics, such as the RDFS-based, description logic-based, Datalog-based semantics. The relationship among the various semantics poses a challenge for the SW community for making the languages interoperable. Institutions provide a means of reasoning about software specifications regardless of the logical system. This makes it an ideal candidate to represent and reason about the various languages in the Semantic Web. In this paper, we construct institutions for the SW languages and use institution morphisms to relate them. We show that RDF framework together with the RDF serializations of SW languages form an indexed institution. This allows the use of Grothendieck institutions to combine Web ontologies described in various languages.
6040880
Rupture degree of graphs
We introduce a new graph parameter, the rupture degree. The rupture degree for a complete graph K n is defined as 1−n, and the rupture degree for an incomplete connected graph G is defined by r(G)=max{ω(G−X)−|X|−m(G−X):X⊂V(G), ω(G−X)>1}, where ω(G−X) is the number of components of G−X and m(G−X) is the order of a largest component of G−X. It is shown that this parameter can be used to measure the vulnerability of networks. Rupture degrees of several specific classes of graphs are determined. Formulas for the rupture degree of join graphs and some bounds of the rupture degree are given. We also obtain some Nordhaus–Gaddum type results for the rupture degree.
24660543
A note on the lower bounds of signed domination number of a graph
Abstract Let G = (V, E) be a graph. For a function f : V → {−1, 1}, the weight of f is w(f) = Σv ∈ V f(v). For a vertex v in V, we define f[v] = Σu∈N[v] f(u). A signed dominating function of G is a function f : V → {−1, 1} such that f[v] ⩾ 1 for all v ∈ V. The signed domination number γs(G) of G is the minimum weight of a signed dominating function on G. A signed dominating function of a weight γs(G) we call a γs-function of G. In this paper, we study the signed domination problem of general graph, and obtain some lower bounds of the signed domination number of a graph, and show that these lower bounds are sharp, and extend a result in Dunbar et al. (1995).
14562465
Bioinformatics on Embedded Systems: A Case Study of Computational Biology Applications on VLIW Architecture
Bioinformatics applications represent the increasingly important workloads. Their characteristics and implications on the underlying hardware design, however, are largely unknown. Currently, biological data processing ubiquitously relies on the high-end systems equipped with expensive, general-purpose processors. The future generation of bioinformatics requires the more flexible and cost-effective computing platforms to meet its rapidly growing market. The programmable, application-specific embedded systems appear to be an attractive solution in terms of easy of programming, design cost, power, portability and time-to-market. The first step towards such systems is to characterize bioinformatics applications on the target architecture. Such studies can help in understanding the design issues and the trade-offs in specializing hardware and software systems to meet the needs of bioinformatics market. This paper evaluates several representative bioinformatics tools on the VLIW based embedded systems. We investigate the basic characteristics of the benchmarks, impact of function units, the efficiency of VLIW execution, cache behavior and the impact of compiler optimizations. The architectural implications observed from this study can be applied to the design optimizations. To the best of our knowledge, this is one of the first such studies that have ever been attempted.