Minimal cycle bases of the lexicographic product of graphs
A construction of minimum cycle bases of the lexicographic product of graphs is presented. Moreover, the length of a longest cycle of a minimal cycle basis is determined.
Minimality of toric arrangements
We prove that the complement of a toric arrangement has the homotopy type of a minimal CW-complex. As a corollary we deduce that the integer cohomology of these spaces is torsionfree. We apply discrete Morse theory to the toric Salvetti complex, providing a sequence of cellular collapses that leads to a minimal complex.
Mnëv's universality theorem revisited.
Modular Substructures in Pseudomodular Lattices.
Multimatroids. II: Orthogonality, minors and connectivity.
Nonrealizability Proofs in Computational Geometry.
Note on the Circuits of a Perfect Matroid Design
Note on the gammoids arising from undirected graphs
Odd cycles and a class of facets of the axial 3-index assignment polytope
On a conjecture concerning dyadic oriented matroids.
On a covering problem of Mullin and Stanton for binary matroids.
On a generalization of the matroid
On a unimodality conjecture in matroid theory.
On certain n-connected matroids.
On P-polynomial representations of projective geometries in algebraic combinatorial geometries.
On sets of vectors of a finite vector space in which every subset of basis size is a basis
It is shown that the maximum size of a set of vectors of a -dimensional vector space over , with the property that every subset of size is a basis, is at most , if , and at most , if , where and is prime. Moreover, for , the sets of maximum size are classified, generalising Beniamino Segre’s “arc is a conic” theorem. These results have various implications. One such implication is that a matrix, with and entries from , has columns which are linearly dependent. Another is...
On Squashed Designs.
On Subgraphs as Matroid Cells.
On sums over partially ordered sets.
On the center of the fundamental group of the complement of a hyperplane arrangement.