13 citations · 23 across the 7 of their papers we have counts for
8 papers
Statistical instability for contracting Lorenz flows
Jose F. Alves, Muhammad Ali Khan
We consider one parameter families of vector fields introduced by Rovella, obtained through modifying the eigenvalues of the geometric Lorenz attractor, replacing the expanding con…
On contact graphs of totally separable domains
Karoly Bezdek, Muhammad A. Khan, Michael Oliwa
Contact graphs have emerged as an important tool in the study of translative packings of convex bodies. The contact number of a packing of translates of a convex body is the number…
Short cycles in digraphs and the Caccetta-Häggkvist conjecture
Muhammad A. Khan
In the theory of digraphs, the study of cycles is a subject of great importance and has given birth to a number of deep questions such as the Behzad-Chartrand-Wall conjecture (1970…
The geometry of homothetic covering and illumination
Karoly Bezdek, Muhammad A. Khan
At a first glance, the problem of illuminating the boundary of a convex body by external light sources and the problem of covering a convex body by its smaller positive homothetic…
Contact numbers for sphere packings
Karoly Bezdek, Muhammad A. Khan
In discrete geometry, the contact number of a given finite number of non-overlapping spheres was introduced as a generalization of Newton's kissing number. This notion has not only…
On the covering index of convex bodies
Karoly Bezdek, Muhammad A. Khan
Covering a convex body by its homothets is a classical notion in discrete geometry that has resulted in a number of interesting and long-standing problems. Swanepoel introduced the…
Equal Sum Sequences and Imbalance Sets of Tournaments
Muhammad Ali Khan
Reid conjectured that any finite set of non-negative integers is the score set of some tournament and Yao gave a non-constructive proof of Reid's conjecture using arithmetic argume…
New lower bounds for the number of blocks in balanced incomplete block designs
Muhammad Ali Khan
Bose proved the inequality for resolvable balanced incomplete block designs (RBIBDs) and Kageyama improved it for RBIBDs which are not affine resolvable. In this note…