Strongly connected orientations and integer lattices (pdf)
Abdi, Cornuéjols, Liu, and Silina Manuscript (2024), to be submitted
Keywords: strongly connected orientation, M-convex set, Hilbert basis, integer lattice, integral basis, Woodall’s conjecture
A min-max theorem for clean tangled clutters (pdf)
Abdi and Cornuéjols Manuscript (2022)
Keywords: clean tangled clutter, min-max theorem, notch, girth, covering number
Published papers
From coordinate subspaces over finite fields to ideal multipartite uniform clutters (pdf)
Abdi and Lee Mathematical Programming (2024) https://doi.org/10.1007/s10107-024-02155-3
Keywords: vector space over finite field, multipartite uniform clutter, ideal clutter, the max-flow min-cut property, minor-closed property, matroid
Abdi, Cornuéjols, Guenin and Tunçel Mathematical Programming 206:125-143 (2024) Extended abstract appeared in IPCO 2022, LNCS 13265, pp. 1-14
Keywords: dyadic linear programming, property testing, Smith normal form, Hilbert basis, circuits, perfect matchings
Testing idealness in the filter oracle model (pdf)
Abdi, Cornuéjols, Guenin and Tunçel Operation Research Letters 50(6):753--755 (2022)
Keywords: Ideal clutter, filter oracle, property testing, cuboid, cube-ideal set, minor
Abdi, Cornuéjols and Palion SIAM Journal on Discrete Mathematics 36(3):2445-2451 (2022)
Keywords: dyadic linear programming, Edmonds-Johnson theorem, Dyadic Conjecture, matching lattice, Petersen graph
Clean clutters and dyadic fractional packings (pdf, talk)
Abdi, Cornuéjols, Guenin and Tunçel SIAM Journal on Discrete Mathematics 36(2):1012-1037 (2022)
Keywords: dyadic linear programming, clean tangled clutter, Dyadic Conjecture, filter oracle, quasi-polynomial time algorithm
Clean tangled clutters, simplices, and projective geometries (pdf)
Abdi, Cornuéjols and Superdock Journal of Combinatorial Theory, Series B 154:60-92 (2022)
Keywords: clean tangled clutter, simplex, projective geometry over GF(2), cuboid, Fano minor
Abdi, Cornuéjols, Huynh and Lee Math Programming 192:29–50 (2022)
Erratum appeared in Math Programming 192:51–55 (2022)
Extended abstract appeared in IPCO 2020, LNCS 12125, pp. 1–12
Keywords: ideal clutter, k-wise intersecting clutter, chromatic number, binary clutter, 8-flow theorem, cuboid
A new infinite family of ideal minimally non-packing clutters (pdf)
Abdi, Cornuéjols and Superdock
Discrete Mathematics 344(7):112413 (2021) Keywords: the τ=2 Conjecture, packing property, cuboid, dijoins
The max-flow min-cut property and ±1-resistant sets (pdf)
Abdi and Cornuéjols Discrete Applied Mathematics 289:455-476 (2020)
Keywords: cuboid, cube-ideal set, resistant set, structure theorem, excluded minor characterization
Abdi, Cornuéjols and Lee Mathematics of Operations Research 46(1):82-114 (2020)
Keywords: cuboid, cube-ideal set, resistant set, polynomial time algorithm, Replication Conjecture, packing property
Abdi, Cornuéjols and Lee Combinatorica 40:605–623 (2020)
Keywords: property testing, polynomial time algorithm, the τ=2 Conjecture, intersecting clutter, clean clutter
Abdi, Cornuéjols, Guričanová and Lee Journal of Combinatorial Theory, Series B 142:144-209 (2020)
Keywords: cuboid, the τ=2 Conjecture, the Flowing Conjecture, the Replication Conjecture, cube-ideal set, strict polarity
Abdi and Guenin Combinatorica 39(4): 753-777 (2019) Extended abstract appeared in IPCO 2017, LNCS 10328, pp. 1–12 Keywords: the Flowing Conjecture, ideal clutter, blocker, Lehman's theorem, signed binary matroid, Fano minor
The minimally non-ideal binary clutters with a triangle (pdf, talk)
Abdi and Guenin Combinatorica 39(4): 719-752 (2019) Keywords: the Flowing Conjecture, Lehman's theorem, blocker, signed binary matroid, Fano minor, odd-K5 minor
Deltas, extended odd holes and their blockers (pdf)
Abdi and Lee Journal of Combinatorial Theory, Series B 136:193-203 (2019) Keywords: Minor, delta, extended odd hole, blocker, filter oracle
Delta minors, delta free clutters, and entanglement (pdf)
Abdi and Pashkovich SIAM Journal on Discrete Mathematics 32(3):1750-1774 (2018) Keywords: convex union,, delta, lift, projection, opposite pair in clutter, blocker
Abdi, Cornuéjols and Pashkovich Mathematics of Operations Research 43(2):533-553 (2018)
Keywords: Ideal clutter, the packing property, the τ=2 Conjecture, cuboid, coexclusive pair in clutter, delta
Abdi, Fukasawa and Sanità Mathematics of Operations Research 43(2):428-459 (2018)
Keywords: Ideal clutter, the packing property, delta, opposite pair in clutter, bidirecting, Steiner tree
Abdi and Guenin Journal of Graph Theory 87:587-652 (2018) Extended abstract appeared in IPCO 2014, LNCS 8494, pp. 1-12
Keywords: the Cycling Conjecture, odd T-join, graphs on surfaces, excluded minor characterization, Fano minor, odd-K5 minor
Lehman's theorem and the directed Steiner tree problem (pdf)
On the mixing set with a knapsack constraint (pdf)
Abdi and Fukasawa Math Programming Series B 157(1):191-217 (2016) Keywords: chance-constrained programming, mixing set, knapsack contraint, facet-defining inequality, extended formulation