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A. Bishnoi

9 records found

A strong blocking set in a finite projective space is a set of points that intersects each hyperplane in a spanning set. We provide a new graph theoretic construction of such sets: combining constant-degree expanders with asymptotically good codes, we explicitly construct strong ...
We prove new upper bounds on the smallest size of affine blocking sets, that is, sets of points in a finite affine space that intersect every affine subspace of a fixed codimension. We show an equivalence between affine blocking sets with respect to codimension-2 subspaces that a ...
A graph G is said to be q-Ramsey for a q-tuple of graphs (H1,..., Hq), denoted by G →q (H1,..., Hq), if every q-edge-coloring of G contains a monochromatic copy of Hi in color i for some i ε [q]. Let sq(H1,..., Hq) denote the smallest m ...
We study the problem of determining the minimum number of affine subspaces of codimension that are required to cover all points of at least times while covering the origin at most times. The case is a classic result of Jamison, which was independently obtained by Brouwer and Schr ...
Given a finite grid in R2, how many lines are needed to cover all but one point at least k times? Problems of this nature have been studied for decades, with a general lower bound having been established by Ball and Serra. We solve this problem for various types of gri ...
We prove that (Formula presented.), where (Formula presented.) is the Ramsey parameter introduced by Burr, Erdős and Lovász in 1976, which is defined as the smallest minimum degree of a graph (Formula presented.) such that any (Formula presented.) -colouring of the edges of (Form ...
A well-known conjecture, often attributed to Ryser, states that the cover number of an r-partite r-uniform hypergraph is at most r−1 times larger than its matching number. Despite considerable effort, particularly in the intersecting case, this conjecture remains wide open, motiv ...