Work

Computing Excluded Minors for Classes of Matroids Representable over Partial Fields

Year: 2024

Type: article

Abstract: We describe an implementation of a computer search for the "small" excluded minors for a class of matroids representable over a partial field. Using these techniques, we enumerate the excluded minors on at most 15 elements for both the class of dyadic matroids, and the class of 2-regular matroids. We conjecture that there are no other excluded minors for the class of 2-regular matroids; whereas, on the other hand, we show that there is a 16-element excluded minor for the class of dyadic matroids.

Source: The Electronic Journal of Combinatorics

DOI: 10.37236/12078

Authors: Nick Brettell, Rudi Pendavingh

Institutions: Victoria University of Wellington, Eindhoven University of Technology

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funders: Marsden Fund, FP7 Ideas: European Research Council

Award: Algorithms for coping with uncertainty and intractability