• Korean Journal of Mathematics
• /
• v.9 no.1
• /
• pp.21-28
• /
• 2001

We find bounds for the domination number of a tournament and investigate the sharpness of these bounds. We also find the domination number of a random tournament.

• Korean Journal of Mathematics
• /
• v.7 no.1
• /
• pp.53-60
• /
• 1999

We find bounds of eigenvalues of bipartite tournament matrices. We see when bipartite matrices exist and how players and teams of the matrices are evenly ranked. Also, we show that a bipartite tournament matrix can be both regular and normal when and only when it has the same team size.

• Bulletin of the Korean Mathematical Society
• /
• v.38 no.1
• /
• pp.183-190
• /
• 2001

In this paper, we look at the spectral bounds of a bipartite tournament matrix M with arbitrary team size. Also we find the condition for the variance of the Perron vector of M to vanish.

• Journal of The Korean Association For Science Education
• /
• v.15 no.1
• /
• pp.27-38
• /
• 1995

The purposes of the 'Students' Science Inquiry Experiment Tournament' which is one of the 'Students' Science Inquiry Olympic Tournaments' are; 1) cultivate students' intellectual interests, inquiry abilities, and scientific attitude dealing with students' scientific reasoning abilities, problem solving abilities, and experimental apparatuses operation abilities. 2) contribute substantiality of science education through experimental inquiry learning. 3) make the ground of basic science development of the future society by selecting excellent students who have talents for science. 4) elevate science teachers' morale by this tournament. The test items set and evaluation results of the tournament were analysed in this study. The results of this study were ; 1) the discrimination ability of the paper-and pencils test and the experiments were low because the students' scores of the items were not normally distributed and standard deviations were very small values. 2) most of the tournament participation students did not answered to the subjective type test items. 3) according to the responses of the tournament participation students, the tournament contribute to the students' interests in science. But the opinion was dominant that the tournament didn't contribute to school science education improvement.

• Journal of the Korean Mathematical Society
• /
• v.49 no.6
• /
• pp.1259-1271
• /
• 2012

We consider a tournament T = (V,A). For each subset X of V is associated the subtournament T(X) = (X,$A{\cap}(X{\times}X)$) of T induced by X. We say that a tournament T' embeds into a tournament T when T' is isomorphic to a subtournament of T. Otherwise, we say that T omits T'. A subset X of V is a clan of T provided that for a, $b{\in}X$ and $x{\in}V{\backslash}X$, $(a,x){\in}A$ if and only if $(b,x){\in}A$. For example, ${\emptyset}$, $\{x\}(x{\in}V)$ and V are clans of T, called trivial clans. A tournament is indecomposable if all its clans are trivial. In 2003, B. J. Latka characterized the class ${\tau}$ of indecomposable tournaments omitting a certain tournament $W_5$ on 5 vertices. In the case of an indecomposable tournament T, we will study the set $W_5$(T) of vertices $x{\in}V$ for which there exists a subset X of V such that $x{\in}X$ and T(X) is isomorphic to $W_5$. We prove the following: for any indecomposable tournament T, if $T{\notin}{\tau}$, then ${\mid}W_5(T){\mid}{\geq}{\mid}V{\mid}$ -2 and ${\mid}W_5(T){\mid}{\geq}{\mid}V{\mid}$ -1 if ${\mid}V{\mid}$ is even. By giving examples, we also verify that this statement is optimal.

• Journal of the Korean Institute of Landscape Architecture
• /
• v.31 no.3
• /
• pp.91-106
• /
• 2003

The objective of this study is to present management methods for Korean golf courses to achieve fast green that satisfies international golf tournament standards during an official golf tournament. The results of both the research and the comparative study on putting green management of 24 tournaments hosted in Korea and 12 tournaments hosted in overseas countries in 2002 are as follows: 1. As for the putting greens in Korean and foreign golf courses where official golf tournaments were held, Korean of official golf tournaments were mainly opened in two-green system golf courses contrary to the foreign cases, and the average size of the greens in Korean golf courses was shown to be greater than that of foreign golf courses to some extent, although there was no difference between the types of turf varieties. 2. Results have shown that unlike foreign golf courses, Korean golf courses were managing putting greens by using greens mowers mostly for general (non-tournament) management, and elaborate rolling attempts failed during official tournament flay week because of an insufficient number of rollers to be input. Therefore, Korean golf courses are required to make efforts to secure 21-inch working-behind greens mowers equipped with tournament bedknifes and 11 blades, which is the greens mowing equipment for professional tournaments, and rollers above all things in order to achieve fast green during tournament play week 3. In attempting to achieve green as fast as that of foreign golf courses, Korean golf courses need to consider the method of performing mowing at 3.0mm height or less with greens mowers for professional tournaments. This needs to be done more than two times, followed by a continuous practice of rolling for proper management.

• Journal of the Korean Mathematical Society
• /
• v.44 no.3
• /
• pp.683-695
• /
• 2007

A tournament is an orientation of a complete graph, and in general a multipartite or c-partite tournament is an orientation of a complete c-partite graph. In a recent article, the authors proved that a regular c-partite tournament with $r{\geq}2$ vertices in each partite set contains a cycle with exactly r-1 vertices from each partite set, with exception of the case that c=4 and r=2. Here we will examine the existence of cycles with r-2 vertices from each partite set in regular multipartite tournaments where the r-2 vertices are chosen arbitrarily. Let D be a regular c-partite tournament and let $X{\subseteq}V(D)$ be an arbitrary set with exactly 2 vertices of each partite set. For all $c{\geq}4$ we will determine the minimal value g(c) such that D-X is Hamiltonian for every regular multipartite tournament with $r{\geq}g(c)$.

• Industrial Engineering and Management Systems
• /
• v.10 no.2
• /
• pp.161-169
• /
• 2011

In seeking further efficiency in production preparation, it is common to examine assembly sequences using digital manufacturing. The assembly sequences affect the product evaluation, so it is necessary to test several assembly sequences before actual production. However, because selection and testing of assembly sequences depends on the operator's personal experience and intuition, only a small number of assembly sequences are actually tested. Nevertheless, there is a systematic method for generating assembly sequences using a contact-related figure. However, the larger the number of parts, the larger the number of assembly sequences geometric becomes. The purpose of this study is to establish a systematic method of generating efficient assembly sequences regardless of the number of parts. To generate such assembly sequences selectively, a "Tournament Tree," which shows the structure of an assembly sequence, is formulated. Applying the method to assembly sequences of a water valve, good assembly sequences with the same structure as the Tournament Tree are identified. The structure of such a Tournament Tree tends to have fewer steps than the others. As a test, the structure is then applied for a drum cartridge with 38 parts. In all the assembly sequences generated from the contact-related figures, the best assembly sequence is generated by using the Tournament Tree.

• 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.

• Journal of applied mathematics & informatics
• /
• v.22 no.1_2
• /
• pp.237-245
• /
• 2006

The set S of distinct scores (outdegrees) of the vertices of a k-partite tournament T($X_l,\;X_2, ..., X_k$) is called its score set. In this paper, we prove that every set of n non-negative integers, except {0} and {0, 1}, is a score set of some 3-partite tournament. We also prove that every set of n non-negative integers is a score set of some k-partite tournament for every $n{\ge}k{\ge}2$.