Ahmad Abdi

activity

20242026

collaborators

5 papers

math.CO2026

Cosigning Crossing Families and Outer-Planar Gadgets

Ahmad Abdi, Mahsa Dalirrooyfard, Meike Neuwohner

Let $F$ be a crossing family over ground set $V$ , that is, for any two sets $U, W \in F$ with nonempty intersection and proper union, both sets $U \cap W, U \cup W$ are in $F$ . Let $…

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

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…

math.CO2024

Strong orientation of a connected graph for a crossing family

Ahmad Abdi, Mahsa Dalirrooyfard, Meike Neuwohner

Given a connected graph $G = (V, E)$ and a crossing family $C$ over ground set $V$ such that $∣ δ_{G} (U) ∣ \geq 2$ for every $U \in C$ , we prove there exists a strong or…

math.CO2024

Strongly connected orientations and integer lattices

Ahmad Abdi, Gérard Cornuéjols, Siyue Liu +1

Let $D = (V, A)$ be a digraph whose underlying undirected graph is $2$ -edge-connected, and let $P$ be the polytope whose vertices are the incidence vectors of arc sets whose reversal…