17086856
A note about shortest cycle covers
Let G be a graph with odd edge-connectivity r. It is proved in this paper that if r>3, then G has a 3-cycle (1,2)-cover of total length at most ((r+1)|E(G)|)/r.
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.
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.
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.
2275334
On strong 1-factors and Hamilton weights of cubic graphs
Abstract A 1-factor M of a cubic graph G is strong if |M∩T|=1 for each 3-edge-cut T of G . It is proved in this paper that a cubic graph G has precisely three strong 1-factors if and only if the graph can be obtained from K 4 via a series of △↔Y operations. Consequently, the graph G admits a Hamilton weight and is uniquely edge-3-colorable.
19566771
Nowhere-Zero 4-Flows and Cayley Graphs on Solvable Groups
We prove that every Cayley graph on a finite solvable group admits a nowhere-zero 4-flow. In particular, every cubic Cayley graph on a solvable group is 3-edge-colorable.
10843699
Efficient feature extraction for 2D/3D objects in mesh representation
Meshes are dominantly used to represent 3D models as they fit well with graphics rendering hardware. Features such as volume, moments, and Fourier transform coefficients need to be calculated from the mesh representation efficiently. We propose an algorithm to calculate these features without transforming the mesh into other representations such as the volumetric representation. To calculate a feature for a mesh, we show that we can first compute it for each elementary shape such as a triangle or a tetrahedron, and then add up all the values for the mesh. The algorithm is simple and efficient, with many potential applications.
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.
17608561
Safety and Hazard Analysis in Concurrent Systems
Safety is a well-known and important class of property of software programs [4] (for instance, partial correctness is a safety property), and of systems in general. The work done here is for the purpose of laying a theoretical and mathematical foundation for allowing static analyses of systems to further safety. States where safety still exists but is liable to be compromised later are further divided into di fferent kinds, with functions giving the nature of the system state. Also considered is a notion of a hazard, which can be informally characterized by saying that hazard exists in safe states that may lead to undesirable events. Details, including proofs of theorems, and further theoretical development (including applications to system composition), may be seen in [8].
207326756
Estimating the amount of defocus through a wavelet transform approach
This paper presents a new technique for defocus estimation of a captured image. In our method, a ratio of the wavelet coefficients of high frequency correspond to a same image point at two different levels is used. For an edge point, it is shown that the ratio is related to the amount of defocus. Let α be the ratio of wavelet coefficients at the first level to that at the second level. The value of α decreases as the amount of defocus increase. In our experiments of iris image analysis, when α is larger than 0.5 the number of feature points in an image almost remain constant. It means that the image is little defocused and available for image recognition. Compared with Fourier methods, this technique is more robust. In addition, this method is fast enough to be used in auto-focus system for tracking moving objects.
29297629
An Application of Fuzzy Cluster analysis to Matchmaking in Middle Agents