مشخصات پژوهش

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 satises White's conjecture if and only if an arbitrary expansion of M does. It follows that it suces to focus on the contraction of a given matroid for checking whether the matroid satises White's conjecture. Finally, some classes of matroids satisfying White's conjecture are presented.