• Bulletin of the Korean Mathematical Society
• /
• v.58 no.1
• /
• pp.31-46
• /
• 2021

Let a and b be positive integers, and let V (G), ��(G), and ��2(G) be the vertex set of a graph G, the minimum degree of G, and the minimum degree sum of two non-adjacent vertices in V (G), respectively. An even [a, b]-factor of a graph G is a spanning subgraph H such that for every vertex v ∈ V (G), dH(v) is even and a ≤ dH(v) ≤ b, where dH(v) is the degree of v in H. Matsuda conjectured that if G is an n-vertex 2-edge-connected graph such that $n{\geq}2a+b+{\frac{a^2-3a}{b}}-2$, ��(G) ≥ a, and ${\sigma}_2(G){\geq}{\frac{2an}{a+b}}$, then G has an even [a, b]-factor. In this paper, we provide counterexamples, which are highly connected. Furthermore, we give sharp sufficient conditions for a graph to have an even [a, b]-factor. For even an, we conjecture a lower bound for the largest eigenvalue in an n-vertex graph to have an [a, b]-factor.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 2000.04a
• /
• pp.52-52
• /
• 2000

• ETRI Journal
• /
• v.30 no.2
• /
• pp.341-343
• /
• 2008

This letter presents an angular minimum spanning tree (AMST) algorithm for topology control in multi-hop wireless ad hoc networks. The AMST algorithm builds up an MST for every angular sector of a given degree around each node to determine optimal transmission power for connecting to its neighbors. We demonstrate that AMST preserves both local and network-wide connectivity. It also improves robustness to link failure and mitigates transmission power waste.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.23 no.61
• /
• pp.33-39
• /
• 2000

In this paper, we present an algorithm for the multicast routing problem when there exit the cell replication limits of ATM switching nodes. This problem can be formulated as a Degree Constrained Minimum Steiner Tree Problem(DCSP). The proposed algorithm is a modification of the shortest path heuristic originally devised for minimum Steiner tree problem. From the experimental results, it can be seen that our algorithm is efficient to obtain a near optimal solution with comparatively low computational time.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.3
• /
• pp.763-787
• /
• 2017

A graph is called 1-planar if it can be drawn in the Euclidean plane ${\mathbb{R}}^2$ such that each edge is crossed by at most one other edge. The weight of an edge is the sum of degrees of two ends. It is known that every planar graph of minimum degree ${\delta}{\geq}3$ has an edge with weight at most 13. In the present paper, we show the existence of edges with weight at most 25 in 3-connected 1-planar graphs.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.15 no.1
• /
• pp.269-276
• /
• 2015

This paper proves the Erd$\ddot{o}$s-Faber-Lov$\acute{a}$sz conjecture of the vertex coloring problem, which is so far unresolved. The Erd$\ddot{o}$s-Faber-Lov$\acute{a}$sz conjecture states that "the union of k copies of k-cliques intersecting in at most one vertex pairwise is k-chromatic." i.e., x(G)=k. In a bid to prove this conjecture, this paper employs a method in which it determines the number of intersecting vertices and that of cliques that intersect at one vertex so as to count a vertex of the minimum degree ${\delta}(G)$ in the Minimum Independent Set (MIS) if both the numbers are even and to count a vertex of the maximum degree ${\Delta}(G)$ in otherwise. As a result of this algorithm, the number of MIS obtained is x(G)=k. When applied to $K_k$-clique sum intersecting graphs wherein $3{\leq}k{\leq}8$, the proposed method has proved to be successful in obtaining x(G)=k in all of them. To conclude, the Erd$\ddot{o}$s-Faber-Lov$\acute{a}$sz conjecture implying that "the k-number of $K_k$-clique sum intersecting graph is k-chromatic" is proven.

• Applied Biological Chemistry
• /
• v.28 no.1
• /
• pp.48-50
• /
• 1985

Moisture requirement for the gelatinization and degree of gelatinization of arrowroot starch were analyzed by X-ray diffractometry. The minimum moisture content for the complete gelatinization of the starch was 45%. The gelatinization of 6% starch suspension was terminated at $75^{\circ}C$.

• 제어로봇시스템학회:학술대회논문집
• /
• 1993.10a
• /
• pp.1213-1218
• /
• 1993

Variable structure control is applied to the robust output tracking control problem of general nonlinear multi-input multi-output (MIMO) systems. Using the concept of relative degree and minimum phase, input/output(I/O) linearization is undertaken. For I/O the linearized system, a new sliding hyperplanes design method is proposed. In this procedure, we can construct very robust and efficient sliding mode controller for general nonlinear systems of relative degree higher than two. The control results are illustrated by adopting a numerical example.

• Proceedings of the Korean Information Science Society Conference
• /
• 2003.04a
• /
• pp.806-808
• /
• 2003

이차원 평면에 주어진 n 개의 점을 연결하는 신장 트리(spanning tree) 중에서, 지름이 최소가 되는 최소지름 신장 트리는 특정 점에서의 분지수가 n-1 까지 증가할 수 있다. 본 논문에서는 트리의 분지수(degree)를 입력으로 받아 그 분지수를 넘지 않는 신장 트리를 구성하면서 트리의 지름은 최소 지름의 상수 배를 넘지 않도록 하는 구성 방법을 제안한다.

• Journal of the Korean Society for Aviation and Aeronautics
• /
• v.16 no.3
• /
• pp.1-6
• /
• 2008

The stalling speed flight test of light airplane, ChangGong-91, was performed to acquire the certification. With power-off engine condition, the wings level stall flight tests were conducted at the aircraft configuration of various flap angle - clean, 20degree, and full flap, respectively. They were performed considering with the combination of the maximum and minimum test weight, and forward and afterward center of gravity. The stalling speeds and the minimum speeds of light airplane were determined from the results of flight test. Also, the appropriateness of stall warning speeds are evaluated through the flight test measures. The airplane is recoverable only with pitch control and engine throttle from stall state without exceptional operation.