scholarly journals The Two-Point Fano and Ideal Binary Clutters

2017 ◽  
pp. 1-12
Author(s):  
Ahmad Abdi ◽  
Bertrand Guenin
Keyword(s):  
Binary Clutters

scholarly journals The Minimally Non-Ideal Binary Clutters with a Triangle

COMBINATORICA ◽  
2019 ◽  
Vol 39 (4) ◽  
pp. 719-752
Author(s):  
Ahmad Abdi ◽  
Bertrand Guenin
Keyword(s):  
Binary Clutters

Ideal Binary Clutters, Connectivity, and a Conjecture of Seymour

2002 ◽  
Vol 15 (3) ◽  
pp. 329-352 ◽  
Author(s):  
Gérard Cornuéjols ◽  
Bertrand Guenin
Keyword(s):  
Binary Clutters

scholarly journals The Two-Point Fano and Ideal Binary Clutters

COMBINATORICA ◽  
2019 ◽  
Vol 39 (4) ◽  
pp. 753-777
Author(s):  
Ahmad Abdi ◽  
Bertrand Guenin
Keyword(s):  
Binary Clutters

scholarly journals Idealness of k-wise intersecting families

2020 ◽  
Author(s):  
Ahmad Abdi ◽  
Gérard Cornuéjols ◽  
Tony Huynh ◽  
Dabeen Lee
Keyword(s):  
Chromatic Number ◽  
Common Element ◽  
Binary Matroids ◽  
Projective Geometries ◽  
Intersecting Families ◽  
Cycle Covers ◽  
Binary Clutters

Abstract A clutter is k-wise intersecting if every k members have a common element, yet no element belongs to all members. We conjecture that, for some integer $$k\ge 4$$ k ≥ 4 , every k-wise intersecting clutter is non-ideal. As evidence for our conjecture, we prove it for $$k=4$$ k = 4 for the class of binary clutters. Two key ingredients for our proof are Jaeger’s 8-flow theorem for graphs, and Seymour’s characterization of the binary matroids with the sums of circuits property. As further evidence for our conjecture, we also note that it follows from an unpublished conjecture of Seymour from 1975. We also discuss connections to the chromatic number of a clutter, projective geometries over the two-element field, uniform cycle covers in graphs, and quarter-integral packings of value two in ideal clutters.

scholarly journals A Characterization of Box 1d-Integral Binary Clutters

1995 ◽  
Vol 65 (2) ◽  
pp. 186-207 ◽  
Author(s):  
A.M.H. Gerards ◽  
M. Laurent
Keyword(s):  
Binary Clutters

The Forbidden Minors of Binary Clutters

1976 ◽  
Vol s2-12 (3) ◽  
pp. 356-360 ◽  
Author(s):  
P. D. Seymour
Keyword(s):  
Forbidden Minors ◽  
Binary Clutters
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