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Idealness of k-wise Intersecting Families

Abdi, Ahmad, Cornuéjols, Gérard, Huynh, Tony and Lee, Dabeen (2020) Idealness of k-wise Intersecting Families. In: Bienstock, Daniel and Zambelli, Giacomo, (eds.) Integer Programming and Combinatorial Optimization - 21st International Conference, IPCO 2020, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer, GBR, pp. 1-12. ISBN 9783030457709

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Identification Number: 10.1007/978-3-030-45771-6_1

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 every 4-wise intersecting clutter is non-ideal. As evidence for our conjecture, we prove it in the binary case. 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 As further evidence for our conjecture, we also note that it follows from an unpublished conjecture of Seymour from 1975.

Item Type: Book Section
Divisions: Mathematics
Date Deposited: 15 May 2020 09:00
Last Modified: 26 Jun 2020 23:07
URI: http://eprints.lse.ac.uk/id/eprint/104419

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