On Diagonally 10-Coloring Plane Triangulations
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: On spanning trees and walks of low maximum degree

title: A note on Vizing's independence number conjecture of edge chromatic critical graphs
abstract: In 1968, Vizing conjectured that, if G is a Δ -critical graph with n vertices, then α ( G ) ⩽ n / 2 , where α ( G ) is the independence number of G. In this note, we verify this conjecture for n ⩽ 2 Δ .

title: On total 9-coloring planar graphs of maximum degree seven
abstract: Given a graph G, a total k-coloring of G is a simultaneous coloring of the vertices and edges ofGwith at most k colors. If ∆(G) is the maximum degree ofG, then no graph has a total ∆-coloring, but Vizing conjectured that every graph has a total (∆ + 2)-coloring. This Total Coloring Conjecture remains open even for planar graphs. This article proves one of the two remaining planar cases, showing that every planar (and projective) graph with ∆ ≤ 7 has a total 9-coloring by means of the discharging method.

title: Coloring edges of graphs embedded in a surface of characteristic zero
abstract: Consider graphs that are embeddable in a surface of characteristic zero. Class two graphs of this type with maximum degree Δ ≤ 6 are known to exist. Hind and Zhao showed that such graphs with maximum degree Δ ge; 8 must be class one. This article shows that such graphs with maximum degree Δ = 7 also must be class one, completing the analysis of these surfaces. These are the first surfaces where the maximum degree of class two graphs has been determined.

title: The size of edge chromatic critical graphs with maximum degree 6
abstract: In 1968, Vizing [ (1968) 117–134;  (1968), 125–142] conjectured that for any edge chromatic critical graph G = (V, E) with maximum degree , |E| ≥ 2{( 1)|V| + 3}. This conjecture has been verified for ≤ 5. In this article, by applying the Contract grant sponsor: Middle Tennessee State University Summer Research Grant 2004;  China University of Mining and Technology Science Council;   National Security Agency; Contract grant number: MDA-904-02-1-0096 ;

title: E-Mail Services on Hybrid P2P Networks
abstract: As one of the most important services of Internet, e-mail is widely used in both commercial business and personal communication. In this paper, we explore ways to develop e-mail systems on P2P networks to overcome the weakness of traditional server-centric e-mail systems. We propose a framework of e-mail system based on hybrid P2P network, and present three implementations of the proposed framework, each of which has different capability, reliability. Our system is more flexible and reliable than the traditional e-mail systems.

title: Identification of Multi-dimensional System based on a Novel Criterion
abstract: A device uses two laser beams to assist in parking a vehicle having a windshield at a desired distance relative to a surface forward of the vehicle, such as the wall of a garage. Independent adjustment means are preferably provided for angling one or both of the first and second beams so as to converge in a localized region of the surface forward of the vehicle when the vehicle is positioned at a desired distance. The preferred embodiment further includes means for mounting the device to a visor within the vehicle, such that the first and second beams pass through the windshield. A momentary contact button on a bottom panel of the enclosure may then be used to activate the laser by squeezing the device against the visor, if so mounted. Within the enclosure there is supported a mirror, prism or other light re-directing element in the path of one of the first and second beams prior to exiting enclosure causing the two beams to converge in a localized region of the wall when the vehicle is parked at a desired distance therefrom. The mirror and beamsplitter are preferably disposed on independently adjustable mounts to assist in fixing the desired distance. As a further option, a dispersive optical element such as a lens may be disposed in the path of one of the first and second beams causing that beam to form a line on the surface forward of the vehicle. Method aspects of the invention are also disclosed.

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: A Working Model for Real-time Interactive Distance Education Support Systems
abstract: In Japan, most of the real time distance learning systems constructed over JGN (Japan Gigabit Network) are simple applications of video conference system equipped with high-quality audio/video transmission equipment. Such systems are not modeled to add distance educational support such as real time floor control, and are insufficient and inefficient to perform real time distance lecture or seminar when the number of sites get larger. This paper proposes a Working Model for distributed computer systems supporting real-time interactive distance lectures or seminars over JGN. As an application of the working model, functions for floor control and tele-presentation were discussed. The utility of the proposed working model was confirmed with an experimental system.

title: MBBNTree Classifier Algorithm Based on Active Learning from Unlabeled Samples
abstract: MBBNTree algorithm, which integrates the advantage of Markov blanket Bayesian networks (MBBN) and decision tree, would behave better performance than other Bayesian networks for classification. But the available training samples with actual classes are not enough for building MBBNTree classifier in practice. Active learning aims at reducing the number of training examples to be labeled by automatically processing the unlabeled examples, then selecting the most informative ones with respect to a given cost function for a human to label. In this paper, the MBBNTree classifier algorithm based on active learning would be presented to solve the problem of learning MBBNTree classifier from unlabeled samples. Experimental results show that the proposed algorithm can reach the same accuracy as passive learning with few labeled training examples.