منابع مشابه
On the critical exponent of transversal matroids
Brylawski [2] has shown that loopless principal transversal matroids have critical exponent at most 2. Welsh [4] asks if a similar result holds for all transversal matroids. We answer in the affirmative by proving that all loopless transversal matroids have critical exponent at most 2. The terminology used here for matroids will in general follow Welsh 131. A rank r transversal matroid M is rep...
متن کاملOn The Density of Binary Matroids Without A Given Minor
This thesis is motivated by the following question: how many elements can a simple binary matroid with no PG(t, 2)-minor have? This is a natural analogue of questions asked about the density of graphs in minor-closed classes. We will answer this question by finding the eventual growth rate function of the class of matroids with no PG(t, 2)-minor, for any t ≥ 2. Our main tool will be the matroid...
متن کاملA density Hales-Jewett theorem for matroids
We show that if α is a positive real number, n and ` are integers exceeding 1, and q is a prime power, then every simple matroid M of sufficiently large rank, with no U2,`-minor, no rank-n projective geometry minor over a larger field than GF(q), and at least αq elements, has a rank-n affine geometry restriction over GF(q). This result can be viewed as an analogue of the multidimensional densit...
متن کاملOn cographic matroids and signed-graphic matroids
We prove that a connected cographic matroid of a graph G is the bias matroid of a signed graph Σ iff G imbeds in the projective plane. In the case that G is nonplanar, we also show that Σ must be the projective-planar dual signed graph of an actual imbedding of G in the projective plane. As a corollary we get that, if G1, . . . , G29 denote the 29 nonseparable forbidden minors for projective-pl...
متن کاملMatroids on convex geometries (cg-matroids)
We consider matroidal structures on convex geometries, which we call cg-matroids. The concept of a cg-matroid is closely related to but different from that of a supermatroid introduced by Dunstan, Ingleton, and Welsh in 1972. Distributive supermatroids or poset matroids are supermatroids defined on distributive lattices or sets of order ideals of posets. The class of cg-matroids includes distri...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2020
ISSN: 1077-8926
DOI: 10.37236/8584