• East Asian mathematical journal
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• v.29 no.3
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• pp.337-347
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• 2013

For an even integer m at least 4 and any positive integer $t$, it is shown that the complete equipartite graph $K_{km(2t)}$ can be decomposed into edge-disjoint gregarious m-cycles for any positive integer ${\kappa}$ under the condition satisfying ${\frac{{(m-1)}^2+3}{4m}}$ < ${\kappa}$. Here it will be called a gregarious cycle if the cycle has at most one vertex from each partite set.

• Journal of the Korea Society of Computer and Information
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• v.20 no.3
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• pp.69-74
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• 2015

This paper offers solutions to unresolved $43{\leq}R(5,5){\leq}49$ and $102{\leq}R(6,6){\leq}165$ problems of Ramsey's number. The Ramsey's number R(s,t) of a complete graph $k_n$ dictates that n-1 number of incidental edges of a arbitrary vertex ${\upsilon}$ is dichotomized into two colors: (n-1)/2=R and (n-1)/2=B. Therefore, if one introduces the concept of distance to the vertex ${\upsilon}$, one may construct a partite graph $K_n=K_L+{\upsilon}+K_R$, to satisfy (n-1)/2=R of {$K_L,{\upsilon}$} and (n-1)/2=B of {${\upsilon},K_R$}. Subsequently, given that $K_L$ forms the color R of $K_{s-1)$, $K_S$ is attainable. Likewise, given that $K_R$ forms the color B of $K_{t-1}$, $K_t$ is obtained. By following the above-mentioned steps, $R(s,t)=K_n$ was obtained, satisfying necessary and sufficient conditions where, for $K_L$ and $K_R$, the maximum distance should be even and incidental edges of all vertices should be equal are satisfied. This paper accordingly proves R(5,5)=43 and R(6,6)=91.

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.747-759
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• 2018

A graph G = (V (G), E(G) of order n = |V (G)| and size m = |E(G)| is said to be odd harmonious if there exists an injection $f:V(G){\rightarrow}\{0,\;1,\;2,\;{\ldots},\;2m-1\}$ such that the induced function $f^*:E(G){\rightarrow}\{1,\;3,\;5,\;{\ldots},\;2m-1\}$ defined by $f^*(uv)=f(u)+f(v)$ is bijection. While a bipartite graph G with partite sets A and B is said to be bigraceful if there exist a pair of injective functions $f_A:A{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ and $f_B:B{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ such that the induced labeling on the edges $f_{E(G)}:E(G){\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ defined by $f_{E(G)}(uv)=f_A(u)-f_B(v)$ (with respect to the ordered partition (A, B)), is also injective. In this paper we prove that odd harmonious graphs and bigraceful graphs are equivalent. We also prove that the number of distinct odd harmonious labeled graphs on m edges is m! and the number of distinct strongly odd harmonious labeled graphs on m edges is [m/2]![m/2]!. We prove that the Cartesian product of strongly odd harmonious trees is strongly odd harmonious. We find some new disconnected odd harmonious graphs.

• International Journal of Computer Science & Network Security
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• v.23 no.1
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• pp.140-146
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• 2023

Resource allocation is one of the top challenges in Internet of Things (IoT) networks. This is due to the scarcity of computing, energy and communication resources in IoT devices. As a result, IoT devices that are not using efficient algorithms for resource allocation may cause applications to fail and devices to get shut down. Owing to this challenge, this paper proposes a novel algorithm for managing computing resources in IoT network. The fog computing devices are placed near the network edge and IoT devices send their large tasks to them for computing. The goal of the algorithm is to conserve energy of both IoT nodes and the fog nodes such that all tasks are computed within a deadline. A bi-partite graph-based algorithm is proposed for stable matching of tasks and fog node computing units. The output of the algorithm is a stable mapping between the IoT tasks and fog computing units. Simulation results are conducted to evaluate the performance of the proposed algorithm which proves the improvement in terms of energy efficiency and task delay.

• Proceedings of the Korean Information Science Society Conference
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• 1999.10b
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• pp.619-621
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• 1999

여러 대의 카메라를 통해 캡춰된 2차원 데이터를 사용하여 3차원의 좌표를 추출하기 위해서는 각 카메라의 2차원 영상 데이터들의 대응점(correpondence point)을 구해야 한다. 이를 위해 에피폴라 제약조건(epipolar constraints)을 이용하여 에피포라 라인(epipolar line)에 근접한 점을 추출할 수 있다. 에피폴라 제약조건을 사용하면, 실제 원하는 점 이외에 많은 수의 고스트(ghost)가 발생할 수 있다. 또한 카메라로부터 은닉(occlusion)된 점들로 인해 모든 카메라에서 대응되는 점이 존재하는지의 여부를 보장할 수 없다. 본 논문에서는 가 카메라의 대응관계를 k-partite graph로 모델링하고, 전역 탐색을 위해 가중치를 적용하여 클릭(clique)을 추출함으로서, 고스트가 제거된 대응점을 구한다.

• Journal of KIISE:Computer Systems and Theory
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• v.27 no.10
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• pp.825-834
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• 2000

광학식 동작 포착(optical motion capture)시스템에서 신뢰할만한 3차원 좌표의 획득과 마커의 궤적 추적은 매우 중요한 문제이다. 3차원 좌표를 획득하기 이해서는 다중의 카메라로부터 2차원의 데이터 간의 대응관계를 구해야 한다. 본 논문에서는 각 카메라에서의 3차원 마커들 간의 대응관계를 k-partite graph로 모델링하고, 릴렉세이션 알고리즘을 사용하여 고스트가 제거된 신뢰성있는 클릭을 추출한다. 이를 통해 정확하고 안정적인 3차원의 좌표를 생성할 수 있다. 또한 추출된 3차원 마커의 궤적의 추적을 위해 칼만 필터를 사용한 마커의 예측과 데이터 연계 문제의 해결을 위한 전략을 제안하고. 사라진 마커의 궤적을 유지시키기 위해 다이나믹 모델을 사용한 추적 알고리즘을 제시한다.