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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2017.1
- 수록면
- 371 - 383 (13page)
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초록· 키워드
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Let M be a matroid. We study the expansions of M mainly to see how thecombinatorial properties of M and its expansions are related to each other. It is shownthat M is a graphic, binary or a transversal matroid if and only if an arbitrary expansionof M has the same property. Then we introduce a new functor, called contraction, whichacts in contrast to expansion functor. As a main result of paper, we prove that a matroidM satis es White's conjecture if and only if an arbitrary expansion of M does. It followsthat it su ces to focus on the contraction of a given matroid for checking whether thematroid satis es White's conjecture. Finally, some classes of matroids satisfying White'sconjecture are presented.
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참고문헌 (21)
참고문헌 신청
A. Schrijver / 2003 / Combinatorial Optimization / Springer-Verlag
B. Sturmfels / 1995 / Grobner Bases and Convex Polytopes / American Mathematical Sociey
C. A. Francisco / 2011 / Coloring of hypergraphs, perfect graphs and associated primes of powers of monomial ideals / J. Algebra 331 : 224 ~ 242
D. J. A. Welsh / 1976 / Matroid Theory / Academic
H. Whitney / 1935 / On the abstract properties of linear dependence / Amer. J. Math. 57 : 509 ~ 533
B. Sturmfels / 1995 / Grobner Bases and Convex Polytopes / American Mathematical Sociey
C. A. Francisco / 2011 / Coloring of hypergraphs, perfect graphs and associated primes of powers of monomial ideals / J. Algebra 331 : 224 ~ 242
D. J. A. Welsh / 1976 / Matroid Theory / Academic
H. Whitney / 1935 / On the abstract properties of linear dependence / Amer. J. Math. 57 : 509 ~ 533
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