18178451
n-Tuple Coloring of Planar Graphs with Large Odd Girth
Abstract. The main result of the papzer is that any planar graph with odd girth at least 10k−7 has a homomorphism to the Kneser graph Gk2k+1, i.e. each vertex can be colored with k colors from the set {1,2,…,2k+1} so that adjacent vertices have no colors in common. Thus, for example, if the odd girth of a planar graph is at least 13, then the graph has a homomorphism to G25, also known as the Petersen graph. Other similar results for planar graphs are also obtained with better bounds and additional restrictions.
17466332
Nowhere-zero 3-flows in products of graphs
A graph G is an odd-circuit tree if every block of G is an odd length circuit. It is proved in this paper that the product of every pair of graphs G and H admits a nowhere-zero 3-flow unless G is an odd-circuit tree and H has a bridge. This theorem is a partial result to the Tutte’s 3-flow conjecture and generalizes a result by Imrich and Skrekovski [7] that the product of two bipartite graphs admits a nowhere-zero 3-flow. A byproduct of this theorem is that every bridgeless Cayley graph G 1⁄4 Cayð ;SÞ on an abelian group with a minimal generating set S admits a nowhere-zero 3-flow except for odd prisms. 2005 Wiley Periodicals, Inc. J Graph Theory 50: 79–89, 2005
46565546
Arc-disjoint circuits in digraphs
11462933
On flows in bidirected graphs
Bouchet conjectured that every bidirected graph which admits a nowhere-zero bidirected flow will admit a nowhere-zero bidirected 6-flow [A. Bouchet, Nowhere-zero integer flows on a bidirected graph, J. Combin. Theory Ser. B 34 (1983) 279-292]. He proved that this conjecture is true with 6 replaced by 216. Zyka proved in his Ph.D dissertation that it is true with 6 replaced by 30. Khelladi proved it is true with 6 replaced with 18 for 4-connected graphs [A. Khelladi, Nowhere-zero integer chains and flows in bidirected graphs, J. Combin. Theory Ser. B 43 (1987) 95-115]. In this paper, we prove that Bouchet's conjecture is true for 6-edge connected bidirected graphs.
13303898
Chords of longest circuits in 3-connected graphs
Thomassen conjectured that every longest circuit of a 3-connected graph has a chord. The conjecture is verified in this paper for projective planar graphs with minimum degree at least 4.
36530209
Determination of the star valency of a graph
The star valency of a graph G is the minimum, over all star decompositions π, of the maximum number of elements in π incident with a vertex. The maximum average degree of G, denoted by dmax-ave(G), is the maximum average degree of all subgraphs of G. In this paper, we prove that the star valency of G is either ⌈dmax-ave(G)/2⌉ or ⌈dmax-ave(G)/2⌉ + 1, and provide a polynomial time algorithm for determining the star valency of a graph.
2983275
The interrelation of TCP responsiveness and smoothness in heterogeneous networks
TCP(/spl alpha/,/spl beta/) protocols trade the congestion window increase value /spl alpha/ for the decrease ratio /spl beta/, to generate smoother traffic patterns and to maintain a friendly behavior. We study the design assumptions of TCP(/spl alpha/,/spl beta/) protocols and discuss the impact of equation-based modulation of /spl alpha/ and /spl beta/ on application efficiency. We confirm experimentally that, in general, smoothness and responsiveness constitute a tradeoff; however, we uncover undesirable dynamics of the protocols when the network or flow characteristics do not follow a prescribed and static behavior. For example, we show that smooth backward adjustments confine the protocol's capability to exploit resources that become available rapidly, and embarrass the fair and efficient growth of incoming flows. Furthermore, we show that in the context of wireless networks with high error rate, a low /spl alpha/ dictates a conservative behavior that degrades the protocol performance with both delay-tolerant and delay-sensitive applications; and in the context of high contention of heterogeneous flows, a low /spl alpha/ does not contribute to efficiency and friendliness.
6853058
Markov chain correlation based clustering of gene expression data
An efficient Markov chain correlation based clustering method (MCC) has been proposed for clustering gene expression data. The gene expression data is first normalized and Markov chains (MC) are constructed from the dynamics of the gene expressions, in which the behavior of the genes at each step of the experiment can be taken into account. Based on the correlation of one-step Markov chain transition probabilities, an agglomerative method is employed to group the series that have similar behavior at each point. The proposed MCC clustering method has been applied to four gene expression datasets to obtain a number of clusters. The results show that the MCC method outperforms the commonly used K-means method and produces clusters that are more meaningful in terms of the similarity of the grouped genes. Another advantage of the proposed method over the existing clustering methods is that the knowledge of the group number is not required.
14923326
Co-histogram and Image Degradation Evaluation
The tool for image degradation evaluation addressed in this paper is called co-histogram, which is a statistic graph generated by counting the corresponding pixel pairs of two images. The graph is a two-dimensional joint probability distribution of the two images. A co-histogram shows how the pixels are distributed among combinations of two image pixel values. By means of co-histogram, we can have a visual understanding of PSNR, and the symmetry of a co-histogram is also significant for objective evaluation of image degradation. Our experiments with image degradation models of image compression, convolution blurring and geometric distortion perform the importance of the co-histogram.
7781593
Kernel based 2D symmetrical principal component analysis for face classification
This paper presents a novel algorithm-kernel based 2D symmetrical principal component analysis (K2DSPCA), which takes full advantage of kernel method, the symmetrical property of facial image and the structural information of image (i.e., the advantage of two-dimensional PCA). Firstly, a facial image is decomposed into an even image and an odd image; Secondly, both the even image and the odd image are mapped to a high dimensional feature space (Reproducing Kernel Hilbert space, RKHS) by a nonlinear function; Thirdly, compute the eigenvectors and the eigenvectors of the even image and the odd image in RKHS, respectively; At last, select the eigenvectors with greater variance as the projection axis. We compare the performance of SPCA, 2DPCA, S2DPCA with K2DSPCA on CBCL database for binary classification, and on ORL face database for multi-category classification, respectively. The experimental results show the K2DSPCA is competitive with or superior to SPCA, 2DPCA and S2DPCA.
40464778
A model for compressing probabilities in belief networks
Probabilistic reasoning with belief (Bayesian) networks is based on conditional probability matrices. Thus it suffers from NP-hard implementations. In particular, the amount of probabilistic information necessary for the computations is often overwhelming. So, compressing the conditional probability table is one of the most important issues faced by the probabilistic reasoning community. Santos suggested an approach (called linear potential functions) for compressing the information from a combinatorial amount to roughly linear in the number of random variable assignments. However, much of the information in Bayesian networks, in which there are no linear potential functions, would be fitted by polynomial approximating functions rather than by reluctantly linear functions. For this reason, we construct a polynomial method to compress the conditional probability table in this paper. We evaluated the proposed technique, and our experimental results demonstrate that the approach is efficient and promising.