• Kyungpook Mathematical Journal
• /
• v.43 no.4
• /
• pp.567-577
• /
• 2003

In this paper, we classify the Steinhaus graphs with minimum degree two.

• Journal of the Korean Mathematical Society
• /
• v.59 no.4
• /
• pp.757-774
• /
• 2022

Let a and b be positive even integers. An even [a, b]-factor of a graph G is a spanning subgraph H such that for every vertex v ∈ V (G), d_H(v) is even and a ≤ dH(v) ≤ b. Let κ(G) be the minimum size of a vertex set S such that G - S is disconnected or one vertex, and let σ₂(G) = min_uv∉E(G) (d(u)+d(v)). In 2005, Matsuda proved an Ore-type condition for an n-vertex graph satisfying certain properties to guarantee the existence of an even [2, b]-factor. In this paper, we prove that for an even positive integer b with b ≥ 6, if G is an n-vertex graph such that n ≥ b + 5, κ(G) ≥ 4, and σ₂(G) ≥ ${\frac{8n}{b+4}}$, then G contains an even [4, b]-factor; each condition on n, κ(G), and σ₂(G) is sharp.

• Proceedings of the Korea Information Processing Society Conference
• /
• 2004.11a
• /
• pp.241-244
• /
• 2004

일반적으로 메쉬(mesh)는 비정규 연결 형태(irregular connectivity)로 되어 있다. 리메싱(remeshing)은 비정규 연결 형태의 메쉬를 정규 연결 형태(regular connectivity)로 바꾸어 주는 작업이다. 메쉬의 기하 정보가 2D 그리드에 저장이 되어 있는 기하이미지(geometry Images)는 비정규 연결 형태의 메쉬를 완전 정규 형태(completely regular connectivity)로 리메싱하는 데 사용된다. 원본 메쉬를 기하 이미지로 생성하는 방법은 변형되는 크기를 최소화 하는 스트레치 메트릭(stretch metric)을 기반으로 이루어 졌다. 이 방법은 리메싱된 메쉬의 언더샘플링(undersampling)을 줄여 주게 된다. 하지만 리메싱 과정에서 생기는 오버샘플링(oversampling)은 줄여 주지 못한다. 본 논문에서는 정점(vertex)의 법선 벡터(normal vector)를 이용하여 기하이미지의 오버샘플링을 줄이는 방법을 제시한다.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.32 no.3C
• /
• pp.256-268
• /
• 2007

In this paper, we present a watermarking method for 3-D mesh sequences. The main idea is to transform vertex norm with the identical connectivity index along temporal axis using wavelet transform and modify the distribution of wavelet coefficients in temporally high (or middle) frequency frames according to watermark bit to be embedded. All vertices are divided into groups, namely bin, using the distribution of coefficients in low frequency frames. As the vertices with the identical connectivity index over whole frames belong to one bin, their wavelet coefficients are also assigned into the same bin. Then, the watermark is embedded into the wavelet coefficients of vertex norm. Due to the use of the distribution, our method can retrieve the hidden watermark without any information about original mesh sequences in the process of watermark detection. Through simulations, we show that the proposed is flirty robust against various attacks that are probably concerned in copyright protection of 3-D mesh sequences.

• Journal of the Korea Computer Graphics Society
• /
• v.14 no.1
• /
• pp.27-33
• /
• 2008

Mobile systems have relatively limited resources such as low memory, slow CPU, or low power comparing to desktop systems. In this paper, we present a new 3D mesh connectivity coding algorithm especially optimized for mobile systems(i.e., mobile phones). By using adaptive octree data structure for vertex positions, a new distance-based connectivity coding is proposed. Our algorithm uses fixed point arithmetic and minimizes dynamic memory allocation, appropriate for mobile systems. We also demonstrate test data to show the utility of our mobile 3D mesh codec.

• Communications of the Korean Mathematical Society
• /
• v.30 no.3
• /
• pp.283-295
• /
• 2015

The atom-bond connectivity index of a graph G (ABC index for short) is defined as the summation of quantities $\sqrt{\frac{d(u)+d(v)-2}{d(u)d(v)}}$ over all edges of G. A cactus graph is a connected graph in which every block is an edge or a cycle. The aim of this paper is to obtain the first and second maximum values of the ABC index among all n vertex cactus graphs.

• 제어로봇시스템학회:학술대회논문집
• /
• 1990.10b
• /
• pp.996-1003
• /
• 1990

We present algebraic algorithms for collision-avoidance robot motion planning problems with planar geometric models. By decomposing the collision-free space into horizontal vertex visibility cells and connecting these cells into a connectivity graph, we represent the global topological structure of collision-free space. Using the C-space obstacle boundaries and this connectivity graph we generate exact (non-heuristic) compliant and gross motion paths of planar curved objects moving with a fixed orientation amidst similar obstacles. The gross motion planning algorithm is further extended (though using approximations) to the case of objects moving with both translational and rotational degrees of freedom by taking slices of the overall orientations into finite segments.

• Journal of the Korean Mathematical Society
• /
• v.36 no.2
• /
• pp.431-445
• /
• 1999

A digraph T is called a local tournament if for every vertex x of T, the set of in-neighbors as well as the set of out-neighbors of in-neighbors of x induce tournaments. Let x and y be two vertices of a 3-connected and arc-3-cyclic local tournament T with y x. We investigate the structure of T such that T contains no (x,y)-path of length k for some k with 3 k V(T) -1. Our result generalized those of [2] and [5] for tournaments.

• Proceedings of the Korean Information Science Society Conference
• /
• 2002.04a
• /
• pp.715-717
• /
• 2002

본 논문은 분할 메쉬의 품질을 향상시키기 위해 초기 메쉬의 위상을 최적화 시키는 MDVC(Modified Dynamic Vertex Connectivity) 알고리즘을 제안한다. 분할 메쉬는 초기 메쉬는 초기 메쉬에 연속적인 분할 규칙이 적용된 메쉬로, 초기 메쉬의 위상에 따라 분할 메쉬의 모양과 부드러움이 좌우된다. 본 논문에서 제안하는 MDVC 알고리즘은 초기 메쉬의 위상과 aspect ratio를 개선시키므로, 기존의 분할 메쉬에서 발생하던 뒤틀림 현상을 방지할 수 있고, 초기 메쉬의 규칙점의 개수가 증가되도록 위상정보를 변경시켜 메쉬분할시 부드러움을 개선시킬 수 있다.

• Journal of the Institute of Electronics Engineers of Korea CI
• /
• v.45 no.3
• /
• pp.160-174
• /
• 2008

In this paper, we propose new coding techniques for photometry data of three-dimensional(3-D) mesh models. We make a good use of geometry and connectivity information to improve coding efficiency of color, normal vector, and texture data. First of all, we determine the coding order of photometry data exploiting connectivity information. Then, we exploit the obtained geometry information of neighboring vortices through the previous process to predict the photometry data. For color coding, the predicted color of the current vertex is computed by a weighted sum of colors for adjacent vortices considering geometrical characteristics between the current vortex and the adjacent vortices at the geometry predictor. For normal vector coding, the normal vector of the current vertex is equal to one of the optimal plane produced by the optimal plane generator with distance equalizer owing to the property of an isosceles triangle. For texture coding, our proposed method removes discontinuity in the texture coordinates and reallocates texture image segments according to the coding order. Simulation results show that the proposed compression schemes provide improved performance over previous works for various 3-D mesh models.