Cookies?
Library Header Image
LSE Research Online LSE Library Services

The two-point Fano and ideal binary clutters

Abdi, Ahmad and Guenin, Bertrand (2019) The two-point Fano and ideal binary clutters. Combinatorica, 39 (4). 753 - 777. ISSN 0209-9683

[img] Text (The two-point Fano and ideal binary clutters) - Accepted Version
Download (864kB)

Identification Number: 10.1007/s00493-018-3779-0

Abstract

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 L 7 , O 5 , LC 7 as a minor. L 7 is the non-ideal clutter of the lines of the Fano plane, O 5 is the non-ideal clutter of odd circuits of the complete graph K 5 , and the two-point FanoLC 7 is the ideal clutter whose sets are the lines, and their complements, of the Fano plane that contain exactly one of two fixed points. In fact, we prove the following stronger statement: if F is a minimally non-ideal binary clutter different from L 7 , O 5 , b(O 5 ) , then through every element, either F or b(F) has a two-point Fano minor.

Item Type: Article
Official URL: https://link.springer.com/journal/493
Additional Information: © 2019 János Bolyai Mathematical Society and Springer-Verlag
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 09 Oct 2019 14:45
Last Modified: 01 Aug 2020 23:00
URI: http://eprints.lse.ac.uk/id/eprint/101842

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics