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The two-point Fano and ideal binary clutters

Abdi, Ahmad ORCID: 0000-0002-3008-4167 and Guenin, Bertrand (2019) The two-point Fano and ideal binary clutters. Combinatorica, 39 (4). 753 - 777. ISSN 0209-9683

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


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
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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 Jun 2024 03:12

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