• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.637-646
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• 2011

Cho and Kim [4] and Kim [6] introduced the concept of the competition index of a digraph. Cho and Kim [4] and Akelbek and Kirkland [1] also studied the upper bound of competition indices of primitive digraphs. In this paper, we study the upper bound of competition indices of strongly connected digraphs. We also study the relation between competition index and ordinary index for a symmetric strongly connected digraph.

• Journal of Korean Society of Forest Science
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• v.97 no.5
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• pp.501-507
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• 2008

The data of crown width with 4 directions, DBH, tree height, and coordinate for sample trees were collected from 30 permanent sample plots in secondary fore st of the Maoershan Experimental Forestry Farm, Northeast China. In this paper, the competition of individual trees in stand were discussed for secondary forest by using iterative Hegyi competition index and crown overlap index that represented the competitive and cooperative interactions among neighboring trees. Active competitors of subject tree in the competition zone were selected to calculate the iterative competition index. Using the results of crown classification based on the equal crown projection area, a new distance dependent competition index called crown overlap index (COI) was developed for secondary forest. The COI performed well in describing the crown competition rather than crown competition factor (CCF). The individual-based competition index discussed in this paper will provide more precise for developing individual tree growth models for secondary forest and it can also use to adjust the stand structure for spatial optimal management.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.65-76
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• 2020

The notion of m-step competition graph was introduced by Cho et al. in 2000 as an interesting variation of competition graph. In this paper, we study the m-step competition graphs of d-partial orders, which generalizes the results obtained by Park et al. in 2011 and Choi et al. in 2018.

• Journal of the Korean Mathematical Society
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• v.42 no.6
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• pp.1251-1264
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• 2005

Let D be an acyclic digraph. The competition graph of D has the same set of vertices as D and an edge between vertices u and v if and only if there is a vertex x in D such that (u, x) and (v, x) are arcs of D. The competition number of a graph G, denoted by k(G), is the smallest number k such that G together with k isolated vertices is the competition graph of an acyclic digraph. It is known to be difficult to compute the competition number of a graph in general. Even characterizing the graphs with competition number one looks hard. In this paper, we continue the work done by Cho and Kim[3] to characterize the graphs with one hole and competition number one. We give a sufficient condition for a graph with one hole to have competition number one. This generates a huge class of graphs with one hole and competition number one. Then we completely characterize the graphs with one hole and competition number one that do not have a vertex adjacent to all the vertices of the hole. Also we show that deleting pendant vertices from a connected graph does not change the competition number of the original graph as long as the resulting graph is not trivial, and this allows us to construct infinitely many graph having the same competition number. Finally we pose an interesting open problem.

• Journal of Arbitration Studies
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• v.15 no.1
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• pp.179-206
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• 2005

The development of information & telecommunication technology and internet-based electronic commerce helps to create a new economic environment. Such an economic environment requires the companies to change themselves, while providing unlimited potential and opportunities to them. Thus, in order to help the companies engaged in a fair and free competition in the electronic market, a fair competition policy needs to be designed and operated. The electronic commerce has not only promote the competition but also impede it. The electronic commerces tend to violate the fair trade than the conventional commerces in terms of differentiation, monopoly, conference, limited competition and intellectual property rights, schumpeterian competition, Alliance competition. With such basic concepts in mind, this study was aimed at reviewing the economic effects of the electronic commerce in the market and addressing the problems involving the application of the fair trade code to the electronic commerce, and thereby, suggesting the insights into our fair competition policy and reform measures.

• KDI Journal of Economic Policy
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• v.29 no.1
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• pp.79-112
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• 2007

Opening domestic market to international trade may enhance not only actual competition but also potential competition from foreign competitors. It seems that the competition authority has focused mainly on the actual competition (measured by the current market share) and has paid less attention to the potential competition. In this regards, this paper investigated the relation between potential foreign competition and domestic market structure. Using dynamic panel regression model, we analyzed the dynamic response of import penetration to the changes of domestic market condition in Korea as a proxy for the degree of potential foreign competition. The empirical results suggests that potential foreign competition does exist in the Korean manufacturing sector and this tendency is more stronger when the market is more concentrated. Thus, in order to effectively implement competition policy, it is necessary to consider both actual and potential competition.

• Journal of the Korean Operations Research and Management Science Society
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• v.30 no.4
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• pp.71-81
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• 2005

This Paper focuses on the effects of outside competition on an optimal echelon base stock level in a two stage supply chain. This is new in that we have been studying the effects of inside competition within a supply chain up to now. It is known that the optimal echelon base stock level with inside competition within a supply chain is less than the global optimal echelon base stock level without inside competition. This is due to the ' public goods ' nature of inventory. That is, more inventory is better, but one wants the other to invest more, thus resulting in under-investment. However, this phenomenon becomes weaker as outside competition increases. We show that as outside competition becomes stronger, the ' public goods ' effects decrease and the optimal echelon base stock level increases. If the level of competition is sufficiently high, the optimal echelon base stock level goes even higher than the global optimal echelon base stock level. We develop a theoretical model for the analysis and conduct a numerical analysis.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.385-396
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• 2008

For a positive integer m and a digraph D, the m-step competition graph $C^m$ (D) of D has he same set of vertices as D and an edge between vertices u and v if and only if there is a vertex x in D such that there are directed walks of length m from u to x and from v to x. Cho and Kim [6] introduced notions of competition index and competition period of D for a strongly connected digraph D. In this paper, we extend these notions to a general digraph D. In addition, we study competition indices of tournaments.

• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.691-702
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• 2011

The competition graph of a digraph D is a graph which has the same vertex set as D and has an edge between x and y if and only if there exists a vertex v in D such that (x, v) and (y, v) are arcs of D. For any graph G, G together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number k(G) of a graph G is defined to be the smallest number of such isolated vertices. In general, it is hard to compute the competition number k(G) for a graph G and it has been one of important research problems in the study of competition graphs. In this paper, we compute the competition numbers of Hamming graphs with diameter at most three.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2001-2011
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• 2013

Cho and Kim [4] have introduced the concept of the competition index of a digraph. Similarly, the competition index of an $n{\times}n$ Boolean matrix A is the smallest positive integer q such that $A^{q+i}(A^T)^{q+i}=A^{q+r+i}(A^T)^{q+r+i}$ for some positive integer r and every nonnegative integer i, where $A^T$ denotes the transpose of A. In this paper, we study the upper bound of the competition index of a Boolean matrix. Using the concept of Boolean rank, we determine the upper bound of the competition index of a nearly reducible Boolean matrix.