The Two-Point Fano and Ideal Binary Clutters

The Two-Point Fano and Ideal Binary Clutters

Let F be a binary clutter. We prove that if F is non-ideal, then either F or its blocker b(F) has one of L7,O5,LC7 as a minor. L7 is the non-ideal clutter of the lines of the Fano plane, O5 is the non-ideal clutter of odd circuits of the complete graph K5, and the two-point Fano LC7 is the ideal clutter whose sets are the lines, and their complements, of the Fano plane that contain exactly one ...

Ideal clutters

Ideal Binary Clutters, Connectivity, and a Conjecture of Seymour

A binary clutter is the family of odd circuits of a binary matroid, that is, the family of circuits that intersect with odd cardinality a fixed given subset of elements. Let A denote the 0;1 matrix whose rows are the characteristic vectors of the odd circuits. A binary clutter is ideal if the polyhedron fx 0 : Ax 1g is integral. Examples of ideal binary clutters are st-paths, st-cuts, T -joins ...

Ideal Binary Clutters, Connectivity, and a Conjecture of Seymour

A binary clutter is the family of odd circuits of a binary matroid, that is, the family of circuits that intersect with odd cardinality a fixed given subset of elements. Let A denote the 0;1 matrix whose rows are the characteristic vectors of the odd circuits. A binary clutter is ideal if the polyhedron fx 0 : Ax 1g is integral. Examples of ideal binary clutters are st-paths, st-cuts, T -joins ...

On Ideal Clutters, Metrics and Multiflows

Abs t rac t . "Binary clutters" contain various objects studied in Combinatorial Optimization, such as paths, Chinese Postman Tours, multiflows and one-sided circuits on surfaces. Minimax theorems about these can be generalized in terms of ideal binary clutters. Seymour has conjectured a characterization of these, and the goal of the present work is to study this conjecture in terms of multiflo...