• Korean Journal of Mathematics
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• v.18 no.4
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• pp.369-380
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• 2010

We give a criterion for vertex extremal length parabolicity of locally finite planar graphs, and use it to show that a disk triangulation graph is circle packing parabolic if and only if its immediate finer graphs are circle packing parabolic.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.345-350
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• 2022

In this work, we confirm a weak version of a conjecture proposed by Hong Wang. The ideal of the work comes from the tree packing conjecture made by Gyárfás and Lehel. Bollobás confirms the tree packing conjecture for many small tree, who showed that one can pack T₁, T₂, …, $T_{n/\sqrt{2}}$ into Kn and that a better bound would follow from a famous conjecture of Erdős. In a similar direction, Hobbs, Bourgeois and Kasiraj made the following conjecture: Any sequence of trees T₁, T₂, …, T_n, with T_i having order i, can be packed into K_n-1,[n/2]. Further Hobbs, Bourgeois and Kasiraj [3] proved that any two trees can be packed into a complete bipartite graph K_n-1,[n/2]. Motivated by the result, Hong Wang propose the conjecture: For each k-partite tree T(𝕏) of order n, there is a restrained packing of two copies of T(𝕏) into a complete k-partite graph B_n+m(𝕐), where $m={\lfloor}{\frac{k}{2}}{\rfloor}$. Hong Wong [4] confirmed this conjecture for k = 2. In this paper, we prove a weak version of this conjecture.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.871-881
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• 2008

In this paper, we study the core stability of the dominating set game which has arisen from the cost allocation problem related to domination problem on graphs. Let G be a graph whose neighborhood matrix is balanced. Applying duality theory of linear programming and graph theory, we prove that the dominating set game corresponding to G has the stable core if and only if every vertex belongs to a maximum 2-packing in G. We also show that for dominating set games corresponding to G, the core is stable if it is large, the game is extendable, or the game is exact. In fact, the core being large, the game being extendable and the game being exact are shown to be equivalent.

• Journal of the Korean Magnetics Society
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• v.4 no.3
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• pp.219-225
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• 1994

The alignment of Sr-ferrite magnetic powders, which is usually related to the fluidity and the applied magnetic field, is investicated in the anisotropic Sr-ferrite / resin-bonded permanent magnets. The magnetic powder alignment is observed to increase with the applied magnetic field and the fluidity which is a function of molding temperature and powder packing ratio. The best magnetic powder alignment is achieved at the following conditions; Sr-ferrite packing ratio of 56vol%, apparent viscosity of about 3000 poise in $1000sec^{-1}$ shear rate, and applied magnetic field of about 5kOe. The degree of preferred orientation of the magnetic powders in the field direction, as determined by the dc hysterisis graphs, is 84~85% (0.84~0.85). This result is in agreement with the value of 0.85 obtained by the X-ray experiments in the $2{\theta}$ range of ${23~40}^0$. The best magnetic properties obtained are:2.2kG of remanent flux density, 2.2MGOe of maximum energy product.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.49 no.4
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• pp.15-25
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• 2012

The research on the FPGA CAD tools in academia has been lacking practicality due to the underlying FPGA fabric architecture which is too simple and inefficient to be applied for commercial FPGAs. Recently, the database of placement positions and routing graphs on commercial FPGA architectures has been built, and provided for enabling the academic development of placement and routing tools. To extend the limit of academic CAD tools even further, we have developed the evaluation toolkit for the K-FPGA architecture which is under development. By providing interface for exchanging data with a commercial FPGA toolkit at every step of mapping, packing, placement and routing in the tool chain, the toolkit enables individual tools to be developed without waiting for the results of the preceding step, and with no dependency on the quality of the results, and compared in detail with commercial tools at any step. Also, the fabric primitive library is developed by extracting the prototype from a reporting file of a commercial FPGA, restructuring it, and modeling the behavior of basic gates. This library can be used as the benchmarking target, and a reference design for new FPGA architectures. Since the architecture is described in a standard HDL which is familiar with hardware designers, and read in the tools rather than hard coded, the tools are "data-driven", and tolerable with the architectural changes due to the design space exploration. The experiments confirm that the developed library is correct, and the functional correctness of applications implemented on the FPGA fabric can be validated by simulation. The placement and routing tools are under development. The completion of the toolkit will enable the development of practical FPGA architectures which, in return, will synergically animate the research on optimization CAD tools.