4956078
Planar Graphs of Maximum Degree Seven are Class I
In 1965, Vizing proved that planar graphs of maximum degree at least eight have the edge chromatic number equal to their maximum degree. He conjectured the same if the maximum degree is either six or seven. This article proves the maximum degree seven case.
22657577
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.
41806675
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. © 1996 John Wiley & Sons, Inc.
6315714
On the edge-reconstruction of graphs embedded in surfaces IV
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.
27555066
On the Edge Reconstruction of Graphs Embedded in Surfaces, III,
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?(?).
38637293
On spanning trees and walks of low maximum degree
16776768
A conceptual model of public medical service system based-on cell phone mobile platform
In recent years, cell phones have played an increasingly important role in rapidly-developing global telecommunication services. At present, mobile business develops very fast. However, the development in other mobile service fields, such as public service, mobile medical service, etc, is still in its infant stage. Drawing on the experience of the ‘doctor workstation project’ which is cooperated by Renmin University of China and Norway Fredskorps Corporation, this paper discusses the research and implementation of the Doctor Workstation System based on cell phone mobile platform. From the practice of the Doctor Workstation System, the paper advances a conceptual model of public medical service system based-on cell phone mobile platform.
5668902
Optimal Spectrum Management in Multiuser Interference Channels
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.
27085331
Design of a real-time interactive tele-exercise classroom for computer exercises over a Gigabit Network
This paper proposes a tele-exercise classroom for computer exercises over the Japan Gigabit Network. The requirements for constructing the tele-exercise classroom be discussed. The main features of the classroom are (1) a teacher can monitor a strident's operations, (2) give instructions to the student, (3) show a demonstration to the student. Besides, exercise materials and/or problems happening during the exercise class can be presented by using a synchronous/asynchronous white board, and discussions between the teacher and a student (students) can be carried out through interactive real-time video/audio. We present a systems model which shows the configuration of the system, user computer terminal types, system modes, and action modes. In addition, the extendibility of the system is considered in the model.
76437
Tibetan Language Continuous Speech Recognition Based on Dynamic Bayesian Network
Dynamic Bayesian Networks (DBN) area subset of the probabilistic graphical models (PGM) which include hidden Markov model (HMM) as a special case. One of the principle weaknesses of HMMs is the independence assumptions on the observed and hidden processes of speech. This paper proposed to use the DBN for Tibetan language continuous speech recognition.The proposed approach is based on structure learning paradigm in DBN framework. This approach has the advantage to guaranty that the resulting model represents speech with higher fidelity than HMM. The results of recognition experiments show that the proposed algorithm has better performance of recognition rate and noise suppression compared with HMM.
39669433
E-Mail Services on Hybrid P2P Networks
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.