A five-color theorem
In this note, we show that the edges and faces of any plane graph with maximum degree three can be simultaneously colored with five colors.

title: On cyclic colorings and their generalizations
abstract: A cyclic coloring is a vertex coloring such that vertices in a face receive different colors. Let Δ be the maximum face degree of a graph. This article shows that plane graphs have cyclic 9 5 Δ -colorings, improving results of Ore and Plummer, and of Borodin. The result is mainly a corollary of a best-possible upper bound on the minimum cyclic degree of a vertex of a plane graph in terms of its maximum face degree. The proof also yields results on the projective plane, as well as for d-diagonal colorings. Also, it is shown that plane graphs with Δ=5 have cyclic 8-colorings. This result and also the 9 5 Δ result are not necessarily best possible.

title: On the Edge Reconstruction of Graphs Embedded in Surfaces, III,
abstract: In this paper, we prove that if a connected graphGembeddable in a surface?of characteristic?(?) satisfies (1) the minimum degree ofG?5, (2) |V(G)|??43?(?), thenGis edge reconstructible. A direct consequence of the above result is that a triangulationGof a surface of characteristic?(?) is edge reconstructible if |V(G)|??43?(?).

title: On the edge-reconstruction of graphs embedded in surfaces IV
abstract: In this paper, by applying the discharging method, we give simple proofs that (1) every n-vertex graph with minimum degree at least 3 and girth at least 5 that is embeddable in a surface Σ of Euler characteristic at least -n/8 is edge-reconstructible, and (2) every n-vertex graph with minimum degree at least 4 that is embeddable without faces of length at most 3 in a surface Σ of Euler characteristic at least -n/6 is edge-reconstructible.

title: On spanning trees and walks of low maximum degree

title: On Diagonally 10-Coloring Plane Triangulations
abstract: This article shows that the vertices of a plane triangulation may be colored with 10 colors such that every pair of vertices has different colors if they are either adjacent or diagonal, that is, that they are not adjacent but are adjacent to two faces which share an edge. This improves a result of Borodin, who showed that 11 colors were sufficient.

title: Silicon Wafer Defect Extraction Based on Morphological Filter and Watershed Algorithm
abstract: Defect extraction techniques are studied regarding the silicon wafer surface defect. We design a new filter based on multiple structuring elements and suggest an improved marker-based and region merging watershed. To begin with, the filter which generalized close-opening and open-closing filter based on the morphological filter with multiple structuring elements is introduced to eliminate the noise and simplify the image and morphological gradient image while preserving the details. And then in order to reduce the over-segmentation of the watershed algorithm, this paper suggests an improved marker-based and region merging method, region average gray value and edge strength criterion is used in merging operation and has a good effect on segmentation. Finally, the improved watershed algorithm is applied to the filtered gradient image to get the defect contours. The experiments show that this method can eliminate the noises and extract accurately location and closed region contours, which lays a good foundation for defect feature extraction and selection.

title: Optimal Spectrum Management in Multiuser Interference Channels
abstract: In this paper, we study the problem of continuous frequency optimal spectrum management in multiuser frequency selective interference channels. We assume that interference is treated as noise by the decoders, and separate encoding is applied. First, a simple pair-wise channel condition for frequency division multiple access schemes to achieve all Pareto optimal points of the rate region is derived. It enables fully distributed global optimal decision making on whether any two users should use orthogonal channels. Next, we present an analytical solution to finding the maximum sum-rate in two-user symmetric frequency flat channels. Generalizing this solution to frequency selective channels, a convex optimization is established that yields the global optimum. Finally, we show that our method generalizes to K-user (K ≥ 2) weighted sum-rate maximization in asymmetric frequency selective channels, and we transform this classic nonconvex optimization to an equivalent convex optimization in the primal domain.

title: A Neighborhood-Based Clustering Algorithm
abstract: In this paper, we present a new clustering algorithm, NBC, i.e., Neighborhood Based Clustering, which discovers clusters based on the neighborhood characteristics of data. The NBC algorithm has the following advantages: (1) NBC is effective in discovering clusters of arbitrary shape and different densities; (2) NBC needs fewer input parameters than the existing clustering algorithms; (3) NBC can cluster both large and high-dimensional databases efficiently.

title: Evolving Model for Small-World Network Based on Benefit Choice
abstract: Based on reviewing the research progress of evolving model for small-world network, the defects of present studies were pointed out. Taking a square grid as the basis, an evolving model for small-world network based on benefit choice was built. This model is different from other papers in which limitation of vector' degree was considered. Then, the author proposed a simulation scheme and compared the network generated by simulation with a same scale random network. The results show that this network has small-world characteristic. Finally, several directions were given.

title: Recursive Algorithms for a Novel Identification Criterion
abstract: A new identification criterion is concerned for disturbed system with color noise in this paper. The cost function considers both the errors between the actual outputs and the estimation result and the difference of each estimation error. Under this performance function, a new recursive algorithm DSCN (Disturbed System with Color Noise) is proposed. It could reduce the influence of noise in system identification, further decrease the prediction error. Several simulation examples are given to illustrate the method's anti-disturbance performance.