Quasi‐graphic matroids * | Zendy

Geelen Jim | Zendy; Gerards Bert | Zendy; Whittle Geoff | Zendy

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Quasi‐graphic matroids *

Author(s) -

Geelen Jim,

Gerards Bert,

Whittle Geoff

Publication year - 2018

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.22177

Subject(s) - matroid , graphic matroid , combinatorics , generalization , mathematics , frame (networking) , discrete mathematics , computer science , mathematical analysis , telecommunications

Frame matroids and lifted‐graphic matroids are two interesting generalizations of graphic matroids. Here, we introduce a new generalization, quasi‐graphic matroids , that unifies these two existing classes. Unlike frame matroids and lifted‐graphic matroids, it is easy to certify that a 3‐connected matroid is quasi‐graphic. The main result is that every 3‐connected representable quasi‐graphic matroid is either a lifted‐graphic matroid or a frame matroid.

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