31784623
Incidence coloring of k-degenerated graphs
Abstract We prove that the incidence coloring number of every k -degenerated graph G is at most Δ ( G )+2 k −1. For K 4 -minor free graphs ( k =2), we decrease this bound to Δ ( G )+2, which is tight. For planar graphs ( k =5), we decrease this bound to Δ ( G )+7.
17776907
Circular perfect graphs
For 1 ≤ d ≤ k, let Kk/d be the graph with vertices 0, 1, · · · , k − 1, in which i ∼ j if d ≤ |i − j| ≤ k − d. The circular chromatic number χc(G) of a graph G is the minimum of those k/d for which G admits a homomorphism to Kk/d. The circular clique number ωc(G) of G is the maximum of those k/d for which Kk/d admits a homomorphism to G. A graph G is circular perfect if for every induced subgraph H of G we have χc(H) = ωc(H). This paper surveys results on circular perfect graphs.
7791840
Pseudo-Hamiltonian-connected graphs
Abstract Given a graph G and a positive integer k , denote by G[k] the graph obtained from G by replacing each vertex of G with an independent set of size k . A graph G is called pseudo- k Hamiltonian-connected if G[k] is Hamiltonian-connected, i.e., every two distinct vertices of G[k] are connected by a Hamiltonian path. A graph G is called pseudo Hamiltonian-connected if it is pseudo- k Hamiltonian-connected for some positive integer k . This paper proves that a graph G is pseudo-Hamiltonian-connected if and only if for every non-empty proper subset X of V(G) , |N(X)|>|X| . The proof of the characterization also provides a polynomial-time algorithm that decides whether or not a given graph is pseudo-Hamiltonian-connected. The characterization of pseudo-Hamiltonian-connected graphs also answers a question of Richard Nowakowski, which motivated this paper.
42953989
The game coloring number of pseudo partial k-trees
Abstract This paper introduces a new class of graphs: (a,b)-pseudo partial k-trees. In some sense, the parameters (a,b) measure a graph's deviation from being a partial k-tree. In particular, a (0,0)-pseudo partial k-tree is just a partial k-tree. We discuss the game coloring number (as well as the game chromatic number) of (a,b)-pseudo partial k-trees, and prove that the game coloring number of an (a,b)-pseudo partial k-tree is at most 3k+2a+b+2. In particular, the game coloring number of a partial k-tree is at most 3k+2. This reduces considerably the previous known upper bound for the game chromatic number of a partial k-tree. Then we describe another strategy for Alice for playing the game, which gives a better upper bound for the game coloring number of (a,b)-pseudo partial 2-trees. Namely, we prove that the game coloring number of an (a,b)-pseudo partial 2-tree is at most a+b+8. By using this result, we prove that the game coloring number of a graph embeddable on an orientable surface of genus g⩾1 is at most ⌊ 1 2 (3 1+48g +23)⌋. This is the first upper bound for the game coloring number of such graphs, and it also improves considerably the previous known upper bound for the game chromatic number of such graphs. Moreover, the strategy for Alice introduced in this paper for playing the game can be considered as a common generalization of the previous known strategies for playing the game on forests, interval graphs, outerplanar graphs and planar graphs.
206792834
Star chromatic numbers of graphs
We investigate the relation between the star-chromatic number χ(G) and the chromatic number χ(G) of a graphG. First we give a sufficient condition for graphs under which their starchromatic numbers are equal to their ordinary chromatic numbers. As a corollary we show that for any two positive integersk, g, there exists ak-chromatic graph of girth at leastg whose star-chromatic number is alsok. The special case of this corollary withg=4 answers a question of Abbott and Zhou. We also present an infinite family of triangle-free planar graphs whose star-chromatic number equals their chromatic number. We then study the star-chromatic number of An infinite family of graphs is constructed to show that for each ε>0 and eachm≥2 there is anm-connected (m+1)-critical graph with star chromatic number at mostm+ε. This answers another question asked by Abbott and Zhou.
5956515
Homomorphisms to oriented paths
Abstract Given an oriented path P , we characterize those digraphs G which are homomorphic to P . The characterization equates the nonexistence of a homomorphism G → P with the existence of a homomorphism W → G , for some oriented path W which is not homomorphic to P . This result complements the recent polynomial time algorithm of Welzl et al. to find such a homomorphism (if one exists).
10041607
Comparison of Modularization Methods in Application to Different Biological Networks
Most biological networks have been proposed to possess modular organization, which increases the robustness, flexibility, and stability of networks. Many clustering methods have been used in mining biological data and partitioning complex networks into functional modules. Most of these methods require presetting the number of modules and therefore can potentially obtain biased results. The Markov clustering method (MCL) and the simulated annealing module-detection method (SA) eliminate this requirement and can objectively separate relatively dense subgraphs. In this paper, we compared these two module-detection methods for three types of biological data: protein family classification, microarray clustering, and modularity of metabolic networks. We found that these two methods show differential advantages for different biological networks. In the case of the gene network based on Affymetrix microarray spike data, MCL exactly identified the same number of groups and same contents in each group set by the spike data. In the case of the gene network derived from actual expression data, although neither of the two methods can perfectly recover the natural classification, MCL performs slightly better than SA. However, with increased random noise added to the gene expression values, SA generates better modular structures with higher modularity. Next we compared the modularization results of MCL and SA for protein family classification and found the modules detected by SA could not be well matched with the Structural Classification of Proteins (SCOP database), which suggests that MCL is ideally suited to the rapid and accurate detection of protein families. In addition, we used both methods to detect modules in the metabolic network of E. coli. MCL gives a trivial clustering, which generates biologically insignificant modules. In contrast, SA detects modules well corresponding to the KEGG functional classification. Moreover the modularity for several other metabolic networks detected by SA is also much higher than that by MCL. In summary, MCL is more suited to modularize relatively complete and definite data, such as a protein family network. In contrast, SA is less sensitive to noise such as experimental error or incomplete data and outperforms MCL when modularizing gene networks based on microarray data and large scale metabolic networks constructed from incomplete databases.
2283419
Nonparametric Transforms of Graph Kernels for Semi-Supervised Learning
We present an algorithm based on convex optimization for constructing kernels for semi-supervised learning. The kernel matrices are derived from the spectral decomposition of graph Laplacians, and combine labeled and unlabeled data in a systematic fashion. Unlike previous work using diffusion kernels and Gaussian random field kernels, a nonparametric kernel approach is presented that incorporates order constraints during optimization. This results in flexible kernels and avoids the need to choose among different parametric forms. Our approach relies on a quadratically constrained quadratic program (QCQP), and is computationally feasible for large datasets. We evaluate the kernels on real datasets using support vector machines, with encouraging results.
205872736
Flatness tolerance evaluation: an approximate minimum zone solution
Abstract This paper is concerned with the problem of flatness tolerance evaluation. First, we introduce the concepts of width and inner radius of point sets, and establish the equivalence between the width of a point set and the inner radius of the convex hull of the self-difference of the set. On this basis, we present an algorithm for calculating the exact minimum zone tolerance of flatness. Second, we prove that an approximation of the inner radius of a convex set can be obtained from the inner radius of the set in fixed direction. On this basis, we present an algorithm for calculating the ‘almost exact’ minimum zone solution. This algorithm is implemented by solving a single linear programming problem, of which the computational complexity is O ( n ). Numerical examples are given to validate the proposed algorithms.
34769702
JavaAHP: a web-based decision analysis tool for natural resource and environmental management
Natural resource and environmental management invariably involves multiple issues, multiple criteria and multiple stakeholders. A large amount of social, economic and environmental information needs to be linked to government policies, stakeholder values, public opinions and management goals. A systematic approach to decision analysis involved in natural resource and environmental management is required to improve the quality of the decision and justify the actions to be taken. The Analytical Hierarchy Process (AHP) provides a methodology for multi-criteria analysis and decision making. It allows critical examination of the underlying assumptions, consistency of the judgements, and facilitates the incorporation of qualitative and subjective considerations into quantitative factors for decision making. JavaAHP is a software tool, which implements the AHP. It uses the AHP methodology to model an environmental problem, evaluate relative desirability of alternatives, and organise the information and judgements used in decision making. JavaAHP is deployed on the World Wide Web (WWW) and can be accessed globally. It takes advantages of the WWW with wide availability, Web resource integration and cross-platform capabilities. This paper introduces the major features of JavaAHP and its potential applications in natural resource and environmental management.
9568730
Exploring video content structure for hierarchical summarization
Abstract.In this paper, we propose a hierarchical video summarization strategy that explores video content structure to provide the users with a scalable, multilevel video summary. First, video-shot- segmentation and keyframe-extraction algorithms are applied to parse video sequences into physical shots and discrete keyframes. Next, an affinity (self-correlation) matrix is constructed to merge visually similar shots into clusters (supergroups). Since video shots with high similarities do not necessarily imply that they belong to the same story unit, temporal information is adopted by merging temporally adjacent shots (within a specified distance) from the supergroup into each video group. A video-scene-detection algorithm is thus proposed to merge temporally or spatially correlated video groups into scenario units. This is followed by a scene-clustering algorithm that eliminates visual redundancy among the units. A hierarchical video content structure with increasing granularity is constructed from the clustered scenes, video scenes, and video groups to keyframes. Finally, we introduce a hierarchical video summarization scheme by executing various approaches at different levels of the video content hierarchy to statically or dynamically construct the video summary. Extensive experiments based on real-world videos have been performed to validate the effectiveness of the proposed approach.