Ahmad Abdi

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20242026

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math.CO2025

The rainbow covering number of clean tangled clutters

Ahmad Abdi, Gérard Cornuéjols

In this brief note, we prove a min-min equality for a clean tangled clutter, that the rainbow covering number is equal to the connectivity of its setcore.

math.CO2025

Integral bases, perfect matchings, and the Petersen graph

Ahmad Abdi, Olha Silina

Let $G = (V, E)$ be a matching-covered graph, denote by $P$ its perfect matching polytope, and by $L$ the integer lattice generated by the integral points in $P$ . In this paper, we gi…

math.CO2025

Lower bounds for cube-ideal set-systems

Ahmad Abdi, Gérard Cornuéjols, Daniel Dadush +1

A set-system $S \subseteq {0, 1}^{n}$ is cube-ideal if its convex hull can be described by capacity and generalized set covering inequalities. In this paper, we use combinatorics, co…