6 papers · 1 filter
Merino-Welsh inequalities for matroids with controlled lattices of cyclic flats
Kolja Knauer, Leonardo Martínez-Sandoval, Criel Merino
Beke, Csáji, Csikvári, and Pituk showed that the Merino--Welsh quotient can be arbitrarily large, so the multiplicative Merino-Welsh inequality…
Counterexamples and symmetry for uneven orthogonal mass partitions in the plane
Leonardo Martínez-Sandoval
Grünbaum asked whether every planar convex body admits, for every , two orthogonal lines cutting it into pieces with cyclically ordered areas . Bá…
The arc chromatic number for Galois projective planes, affine planes and Euclidean grids
Gabriela Araujo-Pardo, Leonardo Martínez-Sandoval
In 1986, Csima and Füredi determined the minimum number of arcs required to partition the points of Galois projective planes and affine planes . We revisit these…
Hamiltonian connectivity of some base-cobase graphs
Leonardo Martínez-Sandoval, Kolja Knauer
There has been wide interest in understanding which properties of base graphs of matroids extend to base-cobase graphs of matroids. A significant result of Naddef and Pulleyblank (…
Equicovering masses in the Euclidean plane
Manuel A. Espinosa-García, Leonardo Martínez-Sandoval, Edgardo Roldán-Pensado
Classic mass partition results are about dividing the plane into regions that are equal with respect to one or more measures (masses). We introduce a new concept in which the notio…
On a colorful problem by Dol'nikov concerning translates of convex bodies
Leonardo Martínez-Sandoval, Edgardo Roldán-Pensado
In this note we study a conjecture by Jerónimo-Castro, Magazinov and Soberón which generalized a question posed by Dol'nikov. Let be families of translates of a…