19646455
The upper bound of essential cyclomatic numbers of hypergraphs
Abstract The essential cyclomatic number of a hypergraph is the maximum number of independent essential cycles of the hypergraph. In this paper, we first prove a general upper bound for the cyclomatic number in terms of the size, order and edge-size of a hypergraph. Then we give a sharp upper bound for ( n −2)-uniform hypergraphs of order n by solving an extremal problem of graphs. It is remarkable that this sharp upper bound is not generally achieved by the complete ( n −2)-uniform hypergraphs.
11520313
Linear Vertex Arboricity, Independence Number and Clique Cover Number
The linear vertex-arboricity of a graph G is defined to the minimum number of subsets into which the vertex-set G can be partitioned so that every subset induces a linear forest. In this paper, we give the upper and lower bounds for sum and product of linear vertex-arboricity with independence number and with clique cover number respectively. All of these bounds are sharp.
206571042
An Upper Bound for the Independent Domination Number
Let G be a simple graph of order n and minimum degree ?. The independent domination number i(G) is defined to be the minimum cardinality among all maximal independent sets of vertices of G. In this paper, we show that i(G)?n+2??2n?. Thus a conjecture of Favaron is settled in the affirmative.
38207892
On the Relations Between Arboricity and Independent Number Or Covering Number
In this paper, the following results are obtained: a(G) + β(G) ⩽ p + 1, ⌈p2⌉ ⩽ a(G)β(G), ⌈p2⌉ ⩽ a′(G) + gb′(G) ⩽ pa′(G) + α′(G) ⩽ 2⌈p2⌉ (δ ⩽ 1) and all bounds are sharp, where p = ¦V(G)¦, ⌈x⌉ denotes the smallest integer greater than or equal to x, a(G) is the vertex arboricity, a′(G) is the edge arboricity, α′(G) is the edge covering number, β(G) is the vertex independent number, β′(G) is the edge independent number, and δ is the minimum degree of G.
6641485
On total covers of graphs
A total cover of a graph G is a subset of V(G)∪E(G) which covers all elements of V(G)∪E(G). The total covering number α2(G) of a graph G is the minimum cardinality of a total cover in G. In [1], it is proven that α2(G)⩽[n2] for a connected graph G of order n. Here we consider the extremal case and give some properties of connected graphs which have a total covering number [n2]. We prove that such a graph with even order has a 1-factor and such a graph with odd order is factor-critical.
24192218
On point-linear arboricity of planar graphs
The point-linear arboricity of a graph G=(V, E), written as p 0 (G), is defined as p 0 (G)=min{k | there exists a partition of V into k subsets, V=∪=1 V i such that (V i ) is a linear forest for 1 >i>k}. In this paper, we will discuss the point-linear arboricity of planar graphs and obtained following results: p 0 (G)=2 if G is a outplanar graph. p 0 (G)=4 if G is a planar graph.
45865876
Graph theoretic characterization and reliability of the generalized Boolean n-cube network
In this paper, a general class of Boolean n-cube structures is investigated. The interconnection is based on a mixed radix number system which results in a variety of generalized Boolean n-cube structures for a given number of processors N = x·2y, where x and y are positive integers. A number of interesting properties of the network are revealed. By a constructive method, the node connectivity of this network is found. Finally, we show that the graph is super-λ and is an optimal reliable structure for interconnection networks.
15835310
An Intuitive Formal Approach to Dynamic Workflow Modeling and Analysis
The increasing dynamics and the continuous changes of business processes raise a challenge to the research and implementation of workflows. The significance of applying formal approaches to the modeling and analysis of workflows has been well recognized and many such approaches have been proposed. However, these approaches require users to master considerable knowledge of the particular formalisms, which impacts the application of these approaches on a larger scale. This paper presents a new formal, yet intuitive approach for the modeling and analysis of workflows, which attempts to overcome the above problem. In addition to the abilities of supporting workflow validation and enactment, this new approach possesses the distinguishing feature of allowing users who are not proficient in formal methods to build up and dynamically modify the workflow models that address their business needs.
8287323
A recurrent neural network for solving linear projection equations
Linear projection equations arise in many optimization problems and have important applications in science and engineering. In this paper, we present a recurrent neural network for solving linear projection equations in real time. The proposed neural network has two layers and is amenable to parallel implementation with simple hardware. In the theoretical aspect, we prove that the proposed neural network can converge globally to the solution set of the problem when the matrix involved in the problem is positive semidefinite and can converge exponentially to a unique solution when the matrix is positive definite. In addition, we analyze the stability of the related dynamic system in detail. As an application, we show that the proposed neural network can be used directly to solve linear and convex quadratic programming problems and linear complementary problems with positive semidefinite matrices. The validity and transient behavior of the neural network are demonstrated by using three numerical examples.
16584684
Diagonal Flips in Labelled Planar Triangulations
Abstract. A classical result of Wagner states that any two (unlabelled) planar triangulations with the same number of vertices can be transformed into each other by a finite sequence of diagonal flips. Recently Komuro gives a linear bound on the maximum number of diagonal flips needed for such a transformation. In this paper we show that any two labelled triangulations can be transformed into each other using at most O(nlogn) diagonal flips. We will also show that any planar triangulation with n>4 vertices has at least n− 2 flippable edges. Finally, we prove that if the minimum degree of a triangulation is at least 4, then it contains at least 2n + 3 flippable edges. These bounds can be achieved by an infinite class of triangulations.
46167609
On solving the face recognition problem with one training sample per subject
The lack of adequate training samples and the considerable variations observed in the available image collections due to aging, illumination and pose variations are the two key technical barriers that appearance-based face recognition solutions have to overcome. It is a well-documented fact that their performance deteriorates rapidly when the number of training samples is smaller than the dimensionality of the image space. This is especially true for face recognition applications where only one training sample per subject is available. In this paper, a recognition framework based on the concept of the so-called generic learning is introduced as an attempt to boost the performance of traditional appearance-based recognition solutions in the one training sample application scenario. Different from contemporary approaches, the proposed solution learns the intrinsic properties of the subjects to be recognized using a generic training database which consists of images from subjects other than those under consideration. Many state-of-the-art face recognition solutions can be readily integrated in the proposed framework. A novel multi-learner framework is also proposed to further boost recognition performance. Extensive experimentation reported in the paper suggests that the proposed framework provides a comprehensive solution and achieves lower error recognition rate when considered in the context of one training sample face recognition problem.