• Honam Mathematical Journal
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• v.38 no.2
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• pp.393-401
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• 2016

In this article, we study the matroid base polytope for a matroid obtained from another matroid by a series or parallel extension of an element. We express this polytope as a wedge of a polytope. In particular, we provide the facial structure of the matroid base polytope corresponding to a series-parallel matroid.

• The Mathematical Education
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• v.13 no.3
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• pp.22-32
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• 1975

Matroid와 transversal theory에 관한 연구가 활발하게 진행되고 있다. 이 논문은 circuit matroid가 transversal이 되기 위한 필요 충분 조건을 지적하고 이를 증명한 것이다. 곧 어떤 graph의 circuit matroid가 transversal이 되기 위한 필요 충분 조건은 그 graph가 graph $K_4$거나 $C_{k}$ $^{2}$에 homeomorphic인 subgraph를 포함하지 않은 것이다. 증명의 방법으로는 주로 matroid의 cocircuit의 성질을 사용하여 transversal Matroid의 presentation을 적절하게 적용하고 graph의 reduction과 contraction을 이용한다.

• Honam Mathematical Journal
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• v.33 no.3
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• pp.381-391
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• 2011

One of the main interesting things of a matroid theory is the representability by a matroid from a matrix over some field F. The representability of uniform matroid $U_{m,n}$ over some field are studied by many authors. In this paper we construct a matrix representing $U_{3,6}$ over the field GF(4). Also we find out matrix of the affine matroid AG(2, 3) over the field GF(4).

• Honam Mathematical Journal
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• v.40 no.1
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• pp.27-46
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• 2018

In this paper, (E, L)-preproximity and uniformity spaces in matriod theory as a generalized to a classical proximity and Uniformity spaces introduced by Csaszar [1] is introduced. Recently, Shi [17]-[18] introduced a new approach to the fuzzification of matroids.Here introduce (E, L)-preproximity and uniformity spaces, Uniformity and strong uniformity on (E, L)-fuzzifying matroid space, Not only study the properties of this new notions, but it has been generated (E, L)-fuzzifying matroid Space from (E, L)-preproximity and uniformity spaces. Next to introduced (E, L)-preproximity continuous in (E, L)-fuzzifying matroid space and used it in more properties. Finally we solve combinatorial optimizations problem via (E, L)-fuzzifying matroid space.

• The Mathematical Education
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• v.12 no.2
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• pp.1-4
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• 1974

Matroid theory, which was first introduced in 1935 by Whitney (2), is a branch of combinational mathematics which has some very much to the fore in the last few years. H. Whitney had just spent several years working in the field of graph theory, and had noticed several similarities between the ideas of independence and rank in graph theory and those of linear independence and dimension in the study of vector spaces. A matroid is essentially a set with some kind of 'independence structure' defined on it. There are several known results concerning how matroids can be induced from given matroid by a digraph. The purpose of this note is to show that, given a matroid M$_{0}$ (N) and a digraph $\Gamma$(N), then a new matroid M(N) is induced, where A⊆N is independent in M(N) if and only if A is the set of initial vertices of a family of pairwise-vertex-disjoint paths with terminal vertices independent in M$_{0}$ (N).(N).

• The Mathematical Education
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• v.16 no.2
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• pp.29-31
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• 1978

bipartite graph와 Euler graph의 정의를 사용하는 대신 이들 graph가 나타내는 특성을 사용하여 bipartite matroid와 Euler matroid를 정의하고 이들 matroid가 binary일 때 서로 dual 의 관계가 있음을 증명한다. 이 관계를 이용하여 bipartite graph와 Euler graph의 성질을 밝힐수 있다.

• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.371-383
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• 2017

Let M be a matroid. We study the expansions of M mainly to see how the combinatorial properties of M and its expansions are related to each other. It is shown that M is a graphic, binary or a transversal matroid if and only if an arbitrary expansion of M has the same property. Then we introduce a new functor, called contraction, which acts in contrast to expansion functor. As a main result of paper, we prove that a matroid M satisfies White's conjecture if and only if an arbitrary expansion of M does. It follows that it suffices to focus on the contraction of a given matroid for checking whether the matroid satisfies White's conjecture. Finally, some classes of matroids satisfying White's conjecture are presented.

• The Mathematical Education
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• v.17 no.2
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• pp.21-23
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• 1979

• Journal of the Korean Mathematical Society
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• v.9 no.1
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• pp.13-14
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• 1972

• The Mathematical Education
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• v.19 no.2
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• pp.11-14
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• 1981