Kyungpook Mathematical Journal

  • 제57권3호
  • /
  • Pages.371-383
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  • 2017
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Expansion and Contraction Functors on Matriods

  • 투고 : 2016.03.25
  • 심사 : 2017.05.26
  • 발행 : 2017.10.23
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초록

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.

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참고문헌

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