Intersecting restrictions in clutters

Abdi, Ahmad ORCID: 0000-0002-3008-4167, Cornuejols, Gerard and Lee, Dabeen (2020) Intersecting restrictions in clutters. Combinatorica, 40 (5). 605 - 623. ISSN 0209-9683

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Abstract

A clutter is intersecting if the members do not have a common element yet every two members intersect. It has been conjectured that for clutters without an intersecting minor, total primal integrality and total dual integrality of the corresponding set covering linear system must be equivalent. In this paper, we provide a polynomial characterization of clutters without an intersecting minor. One important class of intersecting clutters comes from projective planes, namely the deltas, while another comes from graphs, namely the blockers of extended odd holes. Using similar techniques, we provide a poly- nomial algorithm for finding a delta or the blocker of an extended odd hole minor in a given clutter. This result is quite surprising as the same problem is NP-hard if the input were the blocker instead of the clutter.

Item Type:	Article
Official URL:	https://www.springer.com/journal/493
Additional Information:	© 2020 Janos Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	06 Nov 2019 11:12
Last Modified:	04 Oct 2024 06:54
URI:	http://eprints.lse.ac.uk/id/eprint/102394

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