Expansion and Contraction Functors on Matriods
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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.
Abstract
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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