10425168
Adjoint polynomials and chromatically unique graphs
Abstract The aim of this expository paper is to give a survey of the results on chromatically unique graphs obtained by studying their adjoint polynomials.
27925843
Chromaticity of a family of K4-homeomorphs
Abstract We discuss the chromaticity of one family of K 4 -homeomorphs which has exactly 2 adjacent paths of length 1, and give sufficient and necessary condition for the graphs in the family to be chromatically unique.
590214
The Chromaticity of Certain Complete Multipartite Graphs
Abstract.In this paper, we first establish a useful inequality on the minimum real roots of the adjoint polynomials of the complete graphs. By using it, we investigate the chromatic uniqueness of certain complete multipartite graphs. An unsolved problem (i.e., Problem 11), posed by Koh and Teo in Graph and Combin. 6(1990) 259–285, is completely solved by giving it a positive answer. Moreover, many existing results on the chromatic uniqueness of complete multipartite graphs are generalized.
37263695
A complete solution to a conjecture on chromatic uniqueness of complete tripartite graphs
Let P(G,@l) be the chromatic polynomial of a graph G. A graph G is chromatically unique if for any graph H, P(H,@l)=P(G,@l) implies [email protected]?G. Koh, Teo and Chia conjectured that for any integers n and k with n>=k+2>=4, the complete tripartite graph K(n-k,n,n) is chromatically unique. Let K(n,m,r)-S denote the graph obtained by deleting all edges in S from the complete tripartite K(n,m,r). In this paper, we establish that for any positive integer n>=m>=r>=2, the chromatic equivalence class of K(n,m,r) is contained in the family {K(x,y,z)-S|1==2k and k>=2.
17735073
On problems and conjectures on adjointly equivalent graphs
For a graph G, let h(G,x) denote its adjoint polynomial and @b(G) denote the minimum real root of h(G,x). Two graphs H and G are said to be adjointly equivalent if h(H,x)=h(G,x). Let F"1={G|@b(G)>-4} and F"2={G|@b(G)>=-4}. In this paper, we give a necessary and sufficient condition for two graphs H and G in F"i to be adjointly equivalent, where i=1,2. We also solve some problems and conjectures proposed by Dong et al. (Discrete Math. 258 (2002) 303-321).
5589315
Chromatic uniqueness of the complements of certain forests
Abstract A tree is called a tree of T -shape if its degree sequence is (1,1,1,2,2, …, 2,3). In this paper, we prove that the complement of the disjoint union of any number copies of a kind of tree of T -shape is chromatically unique by studying its adjoint polynomial.
44250435
An Adaptive Agent Society for Environmental Scanning through the Internet
Business managers need to promptly respond to environmental changes. Environmental scanners are thus important in discovering and monitoring the information of interest (IOI). In this paper, we explore continuous and resource-bounded environmental scanning (CRBES). The scanner continuously scans for new IOI without consuming too much resource (e.g. bandwidths of computer networks and services of information servers). In that case, new IOI may be discovered in a complete and timely manner without making the related networks and servers too exhausted to provide services. We develop a multiagent framework ACES to achieve CRBES. The agents form an adaptive society by adapting their population and specialty to information needs of individual users, resource limitation of environmental scanning, distribution of IOI in the environments, and update behaviors of the IOI. The delivery of ACES to businesses may constantly provide timelier IOI without causing serious problems to the Intranet and the Internet communities.
22077737
Collaborative Multiagent Adaptation for Business Environmental Scanning Through the Internet
Businesses should promptly respond to their dynamic environments. Environmental scanners are thus essential for the businesses to discover and monitor environmental information of interest (IOI). In this paper, we explore user-centered, continuous and resource-bounded environmental scanning (UCRES). Upon receiving information preferences of managers, new IOI should be continuously detected in a timely and complete manner without consuming too much resource (e.g. bandwidths of computer networks and services of information servers). We develop a multiagent framework AESA to tackle the challenges of UCRES. Each agent is a simple entity. All agents collaboratively adapt their population and resource consumption to several dynamic aspects of UCRES: information preferences of individual users, resource limitation of environmental scanning, distribution of IOI in the environments, and update behaviors of the IOI. The delivery of AESA to businesses may constantly provide a larger amount of important and timely IOI without exhausting the Intranet and the Internet communities.
40972997
Algorithmic Aspects of Topology Control Problems for Ad Hoc Networks
Topology control problems are concerned with the assignment of power values to the nodes of an ad hoc network so that the power assignment leads to a graph topology satisfying some specified properties. This paper considers such problems under several optimization objectives, including minimizing the maximum power and minimizing the total power. A general approach leading to a polynomial algorithm is presented for minimizing maximum power for a class of graph properties called monotone properties. The difficulty of generalizing the approach to properties that are not monotone is discussed. Problems involving the minimization of total power are known to be NP-complete even for simple graph properties. A general approach that leads to an approximation algorithm for minimizing the total power for some monotone properties is presented. Using this approach, a new approximation algorithm for the problem of minimizing the total power for obtaining a 2-node-connected graph is developed. It is shown that this algorithm provides a constant performance guarantee. Experimental results from an implementation of the approximation algorithm are also presented.
9652055
Incremental context mining for adaptive document classification
Automatic document classification (DC) is essential for the management of information and knowledge. This paper explores two practical issues in DC: (1) each document has its context of discussion, and (2) both the content and vocabulary of the document database is intrinsically evolving. The issues call for adaptive document classification (ADC) that adapts a DC system to the evolving contextual requirement of each document category, so that input documents may be classified based on their contexts of discussion. We present an incremental context mining technique to tackle the challenges of ADC. Theoretical analyses and empirical results show that, given a text hierarchy, the mining technique is efficient in incrementally maintaining the evolving contextual requirement of each category. Based on the contextual requirements mined by the system, higher-precision DC may be achieved with better efficiency.
40646883
Adaptive sampling for thresholding in document filtering and classification
Document filtering (DF) and document classification (DC) are often integrated together to classify suitable documents into suitable categories. A popular way to achieve integrated DF and DC is to associate each category with a threshold. A document d may be classified into a category c only if its degree of acceptance (DOA) with respect to c is higher than the threshold of c. Therefore, tuning a proper threshold for each category is essential. A threshold that is too high (low) may mislead the classifier to reject (accept) too many documents. Unfortunately, thresholding is often based on the classifier's DOA estimations, which cannot always be reliable, due to two common phenomena: (1) the DOA estimations made by the classifier cannot always be correct, and (2) not all documents may be classified without any controversy. Unreliable estimations are actually noises that may mislead the thresholding process. In this paper, we present an adaptive and parameter-free technique AS4T to sample reliable DOA estimations for thresholding. AS4T operates by adapting to the classifier's status, without needing to define any parameters. Experimental results show that, by helping to derive more proper thresholds, AS4T may guide various classifiers to achieve significantly better and more stable performances under different circumstances. The contributions are of practical significance for real-world integrated DF and DC.