Ideal clutters

Ideal clutters

On ideal minimally non-packing clutters

We consider the following conjecture proposed by Cornuéjols, Guenin and Margot: every ideal minimally non-packing clutter has a transversal of size 2. For a clutter C, let C̃ denote the set of hyperedges of C which intersect any minimum transversal in exactly one element. We divide the (non-)existence problem of an ideal minimally non-packing clutter D into two steps. In the first step, we give ...

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...

Ideal clutters that do not pack

For a clutter C over ground set E, a pair of distinct edges e, f ∈ E are coexclusive if every minimal cover contains at most one of them. An identification of C is another clutter obtained after identifying coexclusive edges of C. If a clutter is non-packing, then so is any identification of it. Inspired by this observation, and impelled by the lack of a qualitative characterization for ideal m...

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 ...