A characterization of the ternary matroids with no \(M(K_ 4)\)-minor

DOI10.1016/0095-8956(87)90041-4zbMath0585.05005OpenAlexW2008551303MaRDI QIDQ1071023

James G. Oxley

Publication date: 1987

Published in: Journal of Combinatorial Theory. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0095-8956(87)90041-4

zbMATH Keywords

Steiner systemcritical problemternary matroidsexcluded minor descriptionsGF(4)-representable matroidsternary gammoids

Mathematics Subject Classification ID

Combinatorial aspects of matroids and geometric lattices (05B35) Triple systems (05B07)

Related Items (16)

On ternary transversal matroids ⋮ A Generalisation of the Matroid Lift Construction ⋮ Binary matroids without prisms, prism duals, and cubes ⋮ Partitioning into common independent sets via relaxing strongly base orderability ⋮ Detecting minors in matroids through triangles ⋮ Matroids with many common bases. ⋮ On Matroids Representable over 𝐺𝐹(3) and Other Fields ⋮ Ternary paving matroids ⋮ The regular matroids with no 5-wheel minor ⋮ Some extremal connectivity results for matroids ⋮ A characterization of certain excluded-minor classes of matroids ⋮ On an excluded-minor class of matroids ⋮ Adjacency, inseparability, and base orderability in matroids ⋮ On the structure of 3-connected matroids and graphs ⋮ The excluded minors for GF(4)-representable matroids ⋮ On the excluded minors for quaternary matroids

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the intersections of circuits and cocircuits in matroids
• On the matroids representable over \(GF(4)\)
• On ternary transversal matroids
• Decomposition of regular matroids
• Matroid representation over GF(3)
• Envelopes of geometric lattices
• On Reid's characterization of the ternary matroids
• On packing 3-connected restrictions into 3-connected matroids
• A characterisation of binary transversal structures
• Gammoids and transversal matroids
• Twelve points in PG (5, 3) with 95040 self-transformations
• In abstrakten Graphen vorhandene vollständige 4‐Graphen und ihre Unterteilungen
• On the Uniqueness of Matroid Representations Over GF(4)
• The Binary Matroids With No 4-Wheel Minor
• ON MATROID CONNECTIVITY
• On the chromatic number of binary matroids
• Extremal Results and Configuration Theorems for Steiner Systems
• Modular Constructions for Combinatorial Geometries
• An Affine Representation for Transversal Geometries
• COLOURING, PACKING AND THE CRITICAL PROBLEM
• On 3-Connected Matroids
• Connectivity in Matroids
• Comments on bases in dependence structures
• A Combinatorial Model for Series-Parallel Networks
• Induced Matroids
• A Geometrical Characterization of Transversal Independence Structures
• TRANSVERSAL MATROIDS, BASE-ORDERABLE MATROIDS, AND GRAPHS
• On a Class of Matroids Arising From Paths in Graphs

This page was built for publication: A characterization of the ternary matroids with no \(M(K_ 4)\)-minor