Search results for: Černý Conjecture

Authors: Wongsakorn Charoenpanitseri

Abstract:

The total chromatic number χ"(G) of a graph G is the minimum number of colors needed to color the elements (vertices and edges) of G such that no incident or adjacent pair of elements receive the same color Let G be a graph with maximum degree Δ(G). Considering a total coloring of G and focusing on a vertex with maximum degree. A vertex with maximum degree needs a color and all Δ(G) edges incident to this vertex need more Δ(G) + 1 distinct colors. To color all vertices and all edges of G, it requires at least Δ(G) + 1 colors. That is, χ"(G) is at least Δ(G) + 1. However, no one can find a graph G with the total chromatic number which is greater than Δ(G) + 2. The Total Coloring Conjecture states that for every graph G, χ"(G) is at most Δ(G) + 2. In this paper, we prove that the Total Coloring Conjectur for a Δ-claw-free 3-degenerated graph. That is, we prove that the total chromatic number of every Δ-claw-free 3-degenerated graph is at most Δ(G) + 2.

Keywords: Total colorings, the total chromatic number, 3-degenerated.

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Authors: Konstanca Nikolajevic, Nicolas Belanger, David Duvivier, Rabie Ben Atitallah, Abdelhakim Artiba

Abstract:

Finding the optimal 3D path of an aerial vehicle under flight mechanics constraints is a major challenge, especially when the algorithm has to produce real time results in flight. Kinematics models and Pythagorian Hodograph curves have been widely used in mobile robotics to solve this problematic. The level of difficulty is mainly driven by the number of constraints to be saturated at the same time while minimizing the total length of the path. In this paper, we suggest a pragmatic algorithm capable of saturating at the same time most of dimensioning helicopter 3D trajectories’ constraints like: curvature, curvature derivative, torsion, torsion derivative, climb angle, climb angle derivative, positions. The trajectories generation algorithm is able to generate versatile complex 3D motion primitives feasible by a helicopter with parameterization of the curvature and the climb angle. An upper ”motion primitives’ concatenation” algorithm is presented based. In this article we introduce a new way of designing three-dimensional trajectories based on what we call the ”Dubins gliding symmetry conjecture”. This extremely performing algorithm will be soon integrated to a real-time decisional system dealing with inflight safety issues.

Keywords: Aerial robots, Motion primitives, Robotics.

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Authors: Yuan-Hong Ho, Chiung-Ju Huang

Abstract:

Previous studies on political budget cycles (PBCs) implicitly assume the executive has full discretion power over fiscal policy, neglecting the role of checks and balances of the legislature. This paper goes beyond traditional PBCs models and sheds light on the case study of Japan, South Korea, and Taiwan over the 1988-2007 periods. Based on the results, we find no evidence of electoral impacts on the public expenditures in South Korean and Taiwan's congressional elections. We also noted that PBCs are found on Taiwan-s government expenditures during our sample periods. Furthermore, the results also show that Japan-s legislature has a significant checks and balances on government-s expenditures. However, empirical results show that the legislature veto player in Taiwan neither has effect on the reduction of public expenditures, nor has the moderating effect over Taiwan-s political budget cycles, albeit that they are statistically insignificant.We suggest that the existence of PBCs in Taiwan is due to a weaker systemof checks and balances. Our conjecture is that Taiwan either has no legislative veto player or has observed low compliance to the law during the time period examined in our study.

Keywords: Checks and balances, compliance to the law, political budget cycles, veto player.

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Authors: A. M. Qahtani, G. B. Wills, A. M. Gravell

Abstract:

Communicating and managing customers’ requirements in software development projects play a vital role in the software development process. While it is difficult to do so locally, it is even more difficult to communicate these requirements over distributed boundaries and to convey them to multiple distribution customers. This paper discusses the communication of multiple distribution customers’ requirements in the context of customised software products. The main purpose is to understand the challenges of communicating and managing customisation requirements across distributed boundaries. We propose a model for Communicating Customisation Requirements of Multi-Clients in a Distributed Domain (CCRD). Thereafter, we evaluate that model by presenting the findings of a case study conducted with a company with customisation projects for 18 distributed customers. Then, we compare the outputs of the real case process and the outputs of the CCRD model using simulation methods. Our conjecture is that the CCRD model can reduce the challenge of communication requirements over distributed organisational boundaries, and the delay in decision making and in the entire customisation process time.

Keywords: Customisation Software Products, Global Software Engineering, Local Decision Making, Requirement Engineering, Simulation Model.

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