• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.4
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• pp.19-38
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• 2007

Graph theory is becoming increasingly significant as it is applied of mathematics, science and technology. It is being actively used in fields as varied as biochemistry(genomics), electrical engineering(communication networks and coding theory), computer science(algorithms and computation) and operations research(scheduling). The powerful results in other areas of pure mathematics. Rhis paper, besides giving a general outlook of these facts, includes new graph theoretical proofs of Fermat's Little Theorem and the Nielson-Schreier Theorem. New applications to DNA sequencing (the SNP assembly problem) and computer network security (worm propagation) using minimum vertex covers in graphs are discussed. We also show how to apply edge coloring and matching in graphs for scheduling (the timetabling problem) and vertex coloring in graphs for map coloring and the assignment of frequencies in GSM mobile phone networks. Finally, we revisit the classical problem of finding re-entrant knight's tours on a chessboard using Hamiltonian circuits in graphs.

• Journal of the Korea Institute of Military Science and Technology
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• v.18 no.4
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• pp.441-450
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• 2015

The tactical communications network has to be deployed rapidly at military operation area and support the communications between the military command systems and the weapon systems. For that, the frequency assignment is required for backbone wireless links of tactical communications network without frequency interferences. In this paper, we propose a frequency assignment method using net filter discrimination (NFD) and graph coloring to avoid frequency interferences. The proposed method presents frequency assignment problem of tactical communications network as vertex graph coloring problem of a weighted graph. And it makes frequency assignment sequences and assigns center frequencies to communication links according to the priority of communication links and graph coloring. The evaluation shows that this method can assign center frequencies to backbone communication links without frequency interferences. It also shows that the method can improve the frequency utilization in comparison with HTZ-warfare that is currently used by Korean Army.

• Journal of the Korea Society of Computer and Information
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• v.24 no.10
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• pp.57-64
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• 2019

In this paper, we study a polynomially solvable case of the inverse interval graph coloring problem. Given an interval graph associated with a specific interval system, the inverse interval graph coloring problem is defined with the assumption that there is no proper K-coloring for the given interval graph, where K is a fixed integer. The problem is to modify the system of intervals associated with the given interval graph by shifting some of the intervals in such a way that the resulting interval graph becomes K-colorable and the total modification is minimum with respect to a certain norm. In this paper, we focus on the case K = 1 where all intervals associated with the interval graph have length 1 or 2, and interval displacement is only allowed to the righthand side with respect to its original position. To solve this problem in polynomial time, we propose a two-phase algorithm which consists of the sorting and First Fit procedure.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.19 no.9
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• pp.1658-1667
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• 1994

In a cellular mobile communication control system, assignment channel for a call in a cell so as to achieve high spectral efficience is an important problem within limited frequence bandwidth. The spectral efficiency is related to the coloring problem of graph theory in a cellular mobile communication control system. In this paper, we propose channel offset scheme using a graph theory of cellular mobile communication control system and formulate chromatic bandwidth of channel offset system which is related graph coloring problem. From formulated channel assignment problem, we investgate an optimal channel offset scheme of more efficent frequence spectrum and cell design according to channel constitution and give and upper and lower bound for overall srectral bandwidth.

• The KIPS Transactions:PartB
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• v.11B no.2
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• pp.221-226
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• 2004

Ant Colony System(ACS) Algorithm is new meta-heuristic for hard combinational optimization problem. It is a population-based approach that uses exploitation of positive feedback as well as greedy search. Recently, various methods and solutions are proposed to solve optimal solution of graph coloring problem that assign to color for adjacency node($v_i, v_j$) that they has not same color. In this paper introducing ANTCOL Algorithm that is method to solve solution by Ant Colony System algorithm that is not method that it is known well as solution of existent graph coloring problem. After introducing ACS algorithm and Assignment Type Problem, show the wav how to apply ACS to solve ATP And compare graph coloring result and execution time when use existent generating functions(ANT_Random, ANT_LF, ANT_SL, ANT_DSATUR, ANT_RLF method) with ANT_XRLF method that use XRLF that apply Randomize to RLF to solve ANTCOL. Also compare graph coloring result and execution time when use method to add re-search to ANT_XRLF(ANT_XRLF_R) with existent generating functions.

• Journal of Digital Convergence
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• v.20 no.2
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• pp.345-351
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• 2022

For simple undirected graph G=(V,E), L(2,1)-coloring of G is a nonnegative real-valued function f : V → [0,1,…,k] such that whenever vertices x and y are adjacent in G then |f(x)-f(y)|≥ 2 and whenever the distance between x and y is 2, |f(x)-f(y)|≥ 1. For a given L(2,1)-coloring c of graph G, the c-span is λ(c) = max{|c(v)-c(v)||u,v∈V}. L(2,1)-coloring number λ(G) = min{λ(c)} where the minimum is taken over all L(2,1)-coloring c of graph G. In this paper, based on Harary's Theorem, we use Tabu Search to figure out the existence of Hamiltonian Path in a complementary graph and confirmed that if λ(G) is equal to n(=|V|).

• The Pure and Applied Mathematics
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• v.31 no.1
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• pp.57-81
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• 2024

We introduce a new degree reduction method for homogeneous symmetric polynomials on binary variables that generalizes the conventional degree reduction methods on monomials introduced by Freedman and Ishikawa. We also design an degree reduction algorithm for general polynomials on binary variables, simulated on the graph coloring problem for random graphs, and compared the results with the conventional methods. The simulated results show that our new method produces reduced quadratic polynomials that contains less variables than the reduced quadratic polynomials produced by the conventional methods.

• Journal of the Korea Fashion and Costume Design Association
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• v.12 no.2
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• pp.67-73
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• 2010

Whole process of textile printing is made by computer and it remarkably improves environment problem. This digital textile printing is becoming next step environment friendly textile printing method. But, still now range of textile possible for digital textile printing is limited, and also color analysis according to fiber types is not completed. The ink printed on the fabrics through DTP printer can be absorbed and fixed into textile without any blots by pre-treatment using suitable media solution for fabrics types. The chemical formulation of media solution used in the pre-treatment process varies according to the types of textiles and inks for DTP products. First, I studied reference books or articles about color analysis of digital textile printing. Second, I recorded pre-process, printing, post-process and coloring of silk, wool, nylon at same condition. After that, I analyzed $L^*\;a^*\;b^*$, Total K/S, ${\Delta}E$ and studied color intensity and coloring. According to this study, I suggested particular textile special for coloring and manual for affective coloring control. It showed that the performance of the digital printing on the Silk, Wool and Nylon blend fabrics treated by the media solution developed in this study was better than the one treated by the previous media solution for each single inks.

• Journal of Electrical Engineering and Technology
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• v.10 no.5
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• pp.2135-2141
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• 2015

Power line communication (PLC) is one of the major communication technologies in smart grid since it combines good communication capability with easy and simple deployment. As a power network can be modeled as a graph, we propose a vertex coloring based slot reuse scheduling in the time division multiple access (TDMA) period for PLCs. Our objective is to minimize the number of assigned time slots, while satisfying the quality of service (QoS) requirement of each station. Since the scheduling problem is NP-hard, we propose an efficient heuristic scheduling, which consists of repeated vertex coloring and slot reuse improvement algorithms. The simulation results confirm that the proposed algorithm significantly reduces the total number of time slots.

• Journal of Communications and Networks
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• v.15 no.3
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• pp.321-328
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• 2013

In this paper, we present a technique for obtaining conflict-free schedules for real-time automation protocol for industrial Ethernet (RAPIEnet) switches. Mathematical model of the switch is obtained using graph theory. Initially network traffic entry and exit parts in a single RAPIEnet switch are identified, so that a bipartite conflict graph can be constructed. The obtained conflict graph is transformed to three kinds of matrices to be used as inputs for our simulation model, and selection of any of the matrix forms is application-specific. A greedy edge-coloring algorithm is used to schedule the network traffic and to solve the minimum coloring problem. After scheduling, empty slots are identified for forwarding the non real-time traffic of asynchronous devices. Finally, an algorithm for synchronizing the schedules of adjacent switches is proposed using edge-contraction and minors. All simulations were carried out using Matlab.